7*13 = 28, according to About & Costello

[Ali Sada]

Hi everyone,

 

Hope all is well. In this sketch, Lou Costello “proves” that 7 * 13 = 28 (not once but three times, using division, multiplication, and addition.)

 

In 2016, Howard Sporn published a paper titled “Abbott-and-Costello Numbers” in the College Mathematics Journal. He says in the Summary  “ We analyze a mathematical routine from the comedy team of Abbott and Costello and determine all possible numbers that could be used in the joke. We determine a recursive formula and a closed-form expression for the resulting integer sequence, both of which use least common multiples.”

I couldn't download the paper, but according to Google "Sporn’s paper studies all numbers that can fit this kind of fake arithmetic routine. The paper gives the recurrence:

A₁ = 1

and for n ≥ 1,

Aₙ₊₁ = ((n+1)/(n+2)) × LCM(Aₙ, n+2).

This produces:

1, 2, 3, 12, 10, 60, 105, 280, 252, 2520, ...

That is basically OEIS A002944 shifted by one place."

I am wondering if this comment is approprate for A002944:

"This sequence appears in Howard Sporn's paper Abbott-and-Costello Numbers (College Mathematics Journal, 2016). Sporn analyzes the famous Abbott & Costello "7 × 13 = 28" routine, where place value is ignored and multiplication is performed digit-wise. The resulting family of "Abbott-and-Costello numbers" is given by a(n) = lcm(1,2,...,n)/n, i.e., this sequence."

 

Best,

 

Ali

 

 

[Sean A. Irvine]

We do support references and links to popular culture where appropriate, but keep the comment as brief as possible.

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[Ali Sada]

Hi Sean,

Thank you for your response. I really appreciate it. I will add the comment below.

"Howard Sporn showed in Abbott-and-Costello Numbers (2016) that the numbers arising from the Abbott & Costello "7 × 13 = 28" multiplication gag are precisely a(n) = lcm(1,2,...,n)/n, i.e., this sequence."

Best,

Ali 

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[jpallouche.math]

Hi all

I have just sent to Ali Sada a copy of Sporn's paper.
best
jp