[seqfan] help wanted: 10,20,30,40,50,60,70,80,90,100,101,21,...

Marc LeBrun mlb at well.com
Wed Feb 22 22:39:26 CET 2023

[apologies if this is a duplicate]

To my surprise, I find 10,20,30,40,50,60,70,80,90,100,101,21,... is NOT in the OEIS.  

The definition I had in mind was "Next larger integer with the same decimal digits as n."

It is the decimal analog of the base-2 version A057168, "Next larger integer with same binary weight (number of 1 bits) as n."

I'd love to see it in the OEIS, but I don't have time to code up a generator, much less submit a properly complete entry for it.

>> Would someone here be willing to take this on?

It should cross-reference the similar -- but critically different in spirit -- sequence A354049, "The smallest number that includes all the digits of n but does not equal n."

Note that A057168 can be computed using Bill Gosper's elegant algorithm from HAKMEM Item #175.

If there's a decimal version of that code that somehow uses some kind of Lunar arithmetic operations or something, I'd surely love to see it!

Of course the numbers that are NOT in A057168 are simply A000225, "a(n) = 2^n - 1."

Similarly, the integers that are NOT in this proposed sequence are A009994, "Numbers with digits in nondecreasing order."  (So, some more cross-refs needed...)

Then there is the sibling permutation, "Numbers whose digits are not monotonically increasing."

And from that the sequences giving the actual permutations...  And so on... 

Apologies for just sketching this and running away, but alas due to personal limitations I really can't make OEIS-worthy submissions right now, so many thanks to anyone who takes this further.

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