2026

[Harvey P. Dale]

           One among several:

0 + 12*34*5 - 6 - 7 + 8 – 9

           Best,

           Harvey

[Amiram Eldar]

Happy New Year 0! + (1 + 2)^(3 + 4) - 5! + 6*7*(8 - 9)

--
You received this message because you are subscribed to the Google Groups "SeqFan" group.
To unsubscribe from this group and stop receiving emails from it, send an email to seqfan+un...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/seqfan/SJ2PR04MB848541DF9E84CBA4D0A1F36EC6BCA%40SJ2PR04MB8485.namprd04.prod.outlook.com.

[Aitzaz Imtiaz]

1+2+345×6-7×8+9 = 2026

Also found this for 2026! on Wolfram Alpha

[Bob Lyons]

Happy 9 + 8 * 7 * 6! / 5 / 4 - 3 + 2 + 1 + 0!

Bob

On Dec 30, 2025, at 11:51 AM, Aitzaz Imtiaz <aitzazi...@gmail.com> wrote:

1+2+345×6-7×8+9 = 2026

Also found this for 2026! on Wolfram Alpha

To view this discussion visit https://groups.google.com/d/msgid/seqfan/a92d0070-5db5-4b95-83dc-e6d8937f3f55n%40googlegroups.com.

<7454.gif>

[Daniel Mondot]

Happy 9*8 + 7 + (6^5)/4 + 3*(2-1) to you too.

Daniel.

To view this discussion visit https://groups.google.com/d/msgid/seqfan/9BBB8131-612D-4AA8-8561-CC9778619B2B%40gmail.com.

[Tomasz Ordowski]

 Trivial (9+8+7+6+5+4+3+2+1+0)^2+1 

with a lame countdown, but with a smile!

Tom Ordo 

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAD5iKahQJKpwR5U0_52PMmzDT7xZMLU2-Qq3Odo%3DnN_s7aNYow%40mail.gmail.com.

[Daniel Mondot]

To use 45^2, without reusing numbers, you could have done this: (9+8+7*5-4-3)^2+1+0

Daniel.

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAF0qcNOO_s0Tg%2B1Mwr4wG8eGt0qEcHTR_QCZwUvuWgP8HYWCGQ%40mail.gmail.com.

[Ed Pegg]

12×34×5-6-7+8-9  == 2026    

1+2+345×6-7×8+9 == 2026  

1+2+345×6-7×8+9 == 2026  

1+2+3-4 (5-(6+7 (8×9)))  == 2026  

9×8 +7+(6^5)/4 + 3×(2-1) == 2026  

34 (56 + 7) - (8 + 9×12)   == 2026   

0! +(1+2)^(3+4) - 5! +6×7×(8 - 9) == 2026   

9+8×7×6! / 5 / 4 - 3 + 2 + 1 + 0!  == 2026   

1 + 9^3 + 6^4 == 2026    

Round[Cosh[9]/2] == 2026    

FromContinuedFraction[{45, {90}}]  == 2026    

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAD5iKajHKTPPU7y-7X%2Bqjn1kH3hJP5%2B510z0CjdrVwauo6Fq9g%40mail.gmail.com.

[Ed Pegg]

• (12-3)×4×56-7+8+9 = 2026  
  1+2+34×56+7×(8+9) = 2026  
  1+(23×4-56)×7×8+9 = 2026  
  12×3×(4+5)×6-7+89 = 2026  
  1+(23-4×5)×(67+8)×9 = 2026  

[Ed Pegg]

12/3!×4^5+67-89 == 2026  
123/4!×56×7+8+9  == 2026 

[Ed Pegg]

9*8-7+654*3-2+1 == 2026
9+8*7+654*3-2+1 == 2026
987+65*4!/3*2-1 == 2026  
9!/8/7/6+5^4+321 == 2026

[Dave Consiglio]

2^11-2x11 == 2026

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAGog0%2BbMj%2BgFzYrTLArTOmnUSpnT0kDdHsaPT1J3Y5LL6uabzg%40mail.gmail.com.

[Jonas Karlsson]

Feeling Roman:

(M - D - C + L/X)*V + I = MMXXVI

Jonas

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAE7BzueCn9-1xT9zZiF9YN-gUF6dU%2BjObpEEB%3DaLEj7vu3Wd9Q%40mail.gmail.com.

[Ed Pegg]

MVI + DX * C/L  

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CABiOuo_cH3E1A3sAuHTxLrDHN14vw-jzKdi42zLKAzb50pByag%40mail.gmail.com.

[Daniel Mondot]

If I didn't make any mistakes:

With the numbers 6, 5, 4, 3, 2, 1, 0, I'm counting 43 solutions.

And I don't count things like:

2026 = 6-5+(43+2!)^((((((((1+0!)!)!)!)!)!)!)!)!
2026 = 6-5+(43+2!)^(((((((1+0!)!)!)!)!)!)!)!
2026 = 6-5+(43+2!)^((((((1+0!)!)!)!)!)!)!
2026 = 6-5+(43+2!)^(((((1+0!)!)!)!)!)!
2026 = 6-5+(43+2!)^((((1+0!)!)!)!)!
2026 = 6-5+(43+2)^(((1+0!)!)!)!
2026 = 6-5+(43+2)^((1+0!)!)!
2026 = 6-5+(43+2)^(1+0!)!

Which are essentially equivalent to:
2026 = 6-5+(43+2)^(1+0!)

With the numbers 0,1,2,3,4,5,6, I'm counting 5 solutions, and they all involve -3*(45-6!)

Example: 2026 = (0-1)^2-3*(45-6!)

With the numbers 7, 6, 5, 4, 3, 2, 1, 0, I am counting 816 solutions.

Example: 2026 = (7+6+5+4!+3)^2+(1*0)!

With the numbers 0, 1, 2, 3, 4, 5, 6, 7, I am counting 78 solutions.

Example: 2026 = 0+12+3!^4+5+6!-7

With the numbers 8, 7, 6, 5, 4, 3, 2, 1, 0, I am counting 20041 solutions.

Example: 2026 = 8+7*6*(5+43)+2+1*0

With the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, I am counting 1843 solutions.

Example: 2026 = (0-1-2-3)^4-5+6!+7+8

With the numbers 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, I am counting over 300000 solutions.

Example: 2026 = 9-(8+76)*(5+4-32-1)+0!

With the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, I am counting over 4500 solutions.

Example: 2026 = 0+1*(2+34)*56-7+8+9

If someone wants the complete list(s), send me a personal email.

Cheers

PS: Let's say goodbye to  (3-1+4!-1^5)*9^2,

and welcome 3+1-4+1+(5*9)^2

Daniel

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAGog0%2BYLqz6DvgSg41y7L%3DjwOJNiKSsWdnTycnzUb4TAfgZghg%40mail.gmail.com.

[Ed Pegg]

Did you make a  1, 2, 3, 4, 5, 6, 7, 8, 9  list?  If so, I'd like to get that one.

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAD5iKaiJjV8OTr6_MJVmg%3DpEdJxj6KgZ_DEUsaX%3Dw0h9QRQSoQ%40mail.gmail.com.

[Ed Pegg]

I'm amused by the longest one on Daniel's list, using factorials seven times.

1^2 - ((3!)!/(4! + 5!))! + (6 + 7)!/8/9!  

1 - 120  + 2145

On Wed, Dec 31, 2025 at 9:59 PM Daniel Mondot <dmo...@gmail.com> wrote:

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAD5iKaiJjV8OTr6_MJVmg%3DpEdJxj6KgZ_DEUsaX%3Dw0h9QRQSoQ%40mail.gmail.com.

[Daniel Mondot]

We can change that to 8 factorials :

(1^2)! - ((3!)!/(4! + 5!))! + (6 + 7)!/8/9!

But that's precisely what my program was trying not to do (adding a factorial that doesn't change a value)

There were many challenges trying to write a program that generates an exhaustive list of how to generate a particular number from a particular list of numbers:

- trying to avoid making duplicates, avoiding duplicate branches : (1+2)+3 is the same as 1+(2+3)

- figuring out which branch to use, when they could lead to the same result, but one of them might need to rely on a fraction.

- add parentheses when necessary, and only when necessary

- making sure that I don't exceed a maximum value, in my case -2^63 to +2^63-1, for any operation (especially factorial and power)

- making the program as fast as it could be

- debugging the many issues I encountered.

And in the process of writing that, I think I found a bug in GCC. apparently -2^63 divided by -1 causes a floating point error, and it shouldn't.

Daniel.

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAGog0%2BZ0Qy3k2tFWZ72mhcPEqwR5H8xDom%2BodJb3XSS_i%2BHgjw%40mail.gmail.com.

[zzllrr]

2026 = (2²+0²+2²+6²)²+(2+0+2+6)²-(2+0+2+6)

Have fun and Happy new year!

Thanks a lot for the equations below, 

2026 = 0 + 12×34×5 - 6 - 7 + 8 – 9
by Harvey P. Dale

2026 = 0! + (1 + 2)³⁺⁴ - 5! + 6×7×(8 - 9)
by Amiram Eldar

2026 = 1+2+345×6-7×8+9
by Aitzaz Imtiaz

2026 = 9 + 8×7×6!/5/4 - 3 + 2 + 1 + 0!
by Bob Lyons

2026 = (9+8+7×5-4-3)²+1+0
2026 = 9×8 + 7 + 6⁵/4 + 3×(2-1)

by Daniel Mondot

2026 = 1+2+3-4×(5-6-7×8×9)
2026 = 34×(56+7) - (8+9×12)
2026 = (12-3)×4×56-7+8+9
2026 = 1+2+34×56+7×(8+9)
2026 = 1+(23×4-56)×7×8+9
2026 = 12×3×(4+5)×6-7+89
2026 = 1+(23-4×5)×(67+8)×9
2026 = 12/3!×4⁵+67-89
2026 = 123/4!×56×7+8+9

2026 = 9×8-7+654×3-2+1
2026 = 9+8×7+654×3-2+1
2026 = 987+65×4!/3×2-1  
2026 = 9!/8/7/6+5⁴+321

MMXXVI = MVI + DX * C/L

2026 = 1² - ((3!)!/(4! + 5!))! + (6 + 7)!/8/9!  
by Ed Pegg


MMXXVI = (M - D - C + L/X)*V + I
by Jonas Karlsson

2026 = (2²+0²+2²+6²)²+(2+0+2+6)²-(2+0+2+6)

by zzllrr xiaole

Daniel Mondot <dmo...@gmail.com> 于2026年1月1日周四 23:18写道：

--

 小  乐  笑  了  -  2  0  2  6 

zzllrr@Gmail.com

 z  z  l  l  r  r  -  M  M  XX  VI 

If you received this communication by mistake, please don't forward it to anyone else (it may contain confidential or privileged information), please erase all copies of it, including all attachments, and please let the sender know it went to the wrong person. Thanks. 
如果您错误地收到此邮件， 请不要转发给任何人（此邮件含有机密信息并受法律保护），请立即删除此邮件，包括其全部附件。并请告知发件人此邮件被发至错误的收件人。谢谢合作

[Ruud H.G. van Tol]

On 2026-01-04 04:10, zzllrr wrote:
> [...]

> 2026 = 9 + 8×7×6!/5/4 - 3 + 2 + 1 + 0!

> 2026 = (9+8+7×5-4-3)²+1+0
> 2026 = 9×8 + 7 + 6⁵/4 + 3×(2-1)

I think the countdown pattern is desired.

Next, it only needs a beautiful way to convert the algebraic expression
into an integer id, to turn it into a term of a sequence.


A not-so-beautiful way:

? { my
    ( s= "9+8*7*6!/5/4-3+2+1+0!"
    , v= Vecsmall(s)
    , c0= 32
    , c1= vecmax(v)
    );
    v= [ c-c0 |c<-v];
    fromdigits(v, c1-c0+1)
}
% 507354730012284841782464681989


To be beautiful, I think it needs a syntax-parser that builds some
normalized AST,
to then convert the token-tree into a positive integer.

-- Ruud

[M F Hasler]

On Tue, Dec 30, 2025 at 1:35 PM Tomasz Ordowski <tomaszo...@gmail.com> wrote:

 Trivial (9+8+7+6+5+4+3+2+1+0)^2+1 

the +1 is ugly, I'd rather simplify to:

 (9+8+7+6+5+4+3+2+1)² + 0!

-M.

 

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAF0qcNOO_s0Tg%2B1Mwr4wG8eGt0qEcHTR_QCZwUvuWgP8HYWCGQ%40mail.gmail.com.