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August 2008

Abulsme Function in OEIS

As of about 19:30 UTC on Sunday, the Abulsme Function is represented as A105272 in the On-Line Encyclopedia of Integer Sequences.

That sequence in particular traverses the array produced by looking at Abulsme(L,S) for all valid combinations of L and S starting with Abulsme(1,1); Abulsme(2,1); Abulsme(2,2); Abulsme(3,1); Abulsme(3,2); Abulsme(3,3); Abulsme(4,1); Abulsme(4,2); Abulsme(4,3); Abulsme(4,4); Abulsme(5,1); etc… In this way you get one infinite sequence with all values of the function.

Some other infinite sequences generated from the function by fixing S and increasing L (starting with L=S) have also been included.

The cases for S=1 and S=2 matched sequences already in the OEIS:

  • S=1: A000012 (The all 1’s sequence)
  • S=2: A024222 (Perfect faro shuffles with cut required to return a deck of size n to original order)

Higher values of S yielded sequences new to the OEIS though:

Only these have been added, although of course sequences can be generated with any positive integer S. These sequences do reach a limit with increasing S though, and the limit of the sequence has been added to the OEIS as well.

Woo! My mathematical masterpiece first documented when I was in 8th grade, and further expounded on from then until around my Freshman year of college, and basically untouched since then… which would be about 17 or 18 years now… is finally recognized. :-)

A certain person with the initials JPS once suggested that the Abulsme Function, when combined with 12 dimensional contour integration, could be used to go back and time and prevent the Space Shuttle Challenger from exploding.

Um… no.

But it is in the OEIS now.

Which is great.

Oh, and I should add, you can even listen to the sequence. I particularly like it when played by a marimba. It has now been added to my iTunes library. :-)