Possible sequences

[John Mason]

Dear all,

Are these interesting enough?

Numbers that have a base 10 representation in which, for any digit d (1 <= d <= 9), the number of occurrences of d is >= the number of occurrences of d-1.

9, 89, 98, 99, 789, 798, 879, 897, 899, 978, 987, 989, 998, 999, 6789, 6798, 6879, 6897, 6978, 6987, 7689, 7698, 7869, 7896, 7899, 7968, 7986, 7989, 7998, 8679, 8697, 8769, 8796, 8799, 8899, 8967, 8976, 8979, 8989, 8997, 8998, 8999, 9678, 9687, 9768, 9786, 9789, 9798, 9867, 9876, 9879, 9889, 9897, 9898, 9899

Numbers that have a base 10 representation in which, for any digit d (1 <= d <= 9), the number of occurrences of d-1 is >= the number of occurrences of d.
0, 10, 100, 102, 120, 201, 210, 1000, 1001, 1002, 1010, 1020, 1023, 1032, 1100, 1200, 1203, 1230, 1302, 1320, 2001, 2010, 2013, 2031, 2100, 2103, 2130, 2301, 2310, 3012, 3021, 3102, 3120, 3201, 3210

john

[Allan Wechsler]

In base 2, the corresponding sequences are A072601 and A072602. If we make the inequality sharp, we get A072600 and A072603.

So this proposal passes at least one of my tests for notability of digit-based sequences. ("Do we have the binary equivalent already?")

 

-- Allan

--
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/CAE1JqoDjHftyP-YA-Bz6iuVnBGy2SspakcC%2B%2B4_0%3DtU-TW2XYA%40mail.gmail.com.

[M F Hasler]

And in base 3 it would be 

A370856 : Numbers m such that c(0) <= c(1) <= c(2), where c(k) = number of k's in the ternary representation of m.

resp.

A370873 : Positive integers m such that c(0) >= c(1) >= c(2), where c(k) = number of k's in the ternary representation of m.
which were added by Clark Kimberling in March 2024

In Crossrefs are the A-numbers for the "strong inequality" analogs.

For base 4 we'd get  3, 11, 14, 15, 27, 30, 39, 45, 47, 54, 57, 59, 62, 63, 75, 78, 99, ....

resp. 0, 4, 16, 18, 24, 33, 36, 64, 65, 66, 68, 72, 75, 78, 80, 96, 99 ...

which seem not yet in the OEIS.

Probably similar for other bases 5 ... 9.

- Maximilian

[John Mason]

Thanks both. 

A394774, A394775 submitted.

I did not submit the "strictly" versions.

The first sequence would become : Numbers that have a base 10 representation in which, for any digit d (1 <= d <= 9), the number of occurrences of d is > the number of occurrences of d-1.

Which would need a first term 122333444455555666666777777788888888999999999.

It would have to be rewritten something like: Numbers that have a base 10 representation in which, for any digit d (1 <= d <= 9) with at least one occurrence, the number of occurrences of d is > the number of occurrences of d-1; also, if d is absent then d-1 is absent too.

john

--

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/CAFqvfd-hg%3DLRvKxvqGm%2BoqQpd3y523KyObKDDy010n4B3J_C5w%40mail.gmail.com.