A231719 After zero, a(n) = largest m such that m! divides the difference between successive nodes A219666(n-1) and A219666(n) in the infinite trunk of the factorial beanstalk.

0, 1, 1, 1, 2, 1, 2, 1, 3, 2, 1, 2, 1, 1, 3, 2, 2, 1, 3, 1, 2, 1, 3, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 3, 2, 2, 1, 3, 1, 2, 1, 3, 1, 1, 1, 3, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 1, 3, 1, 1, 1, 3, 2, 3, 2, 2, 1, 2, 1, 2, 1, 3, 1, 1, 1, 3, 2, 3, 2, 2, 1, 2, 3, 2, 1, 1, 1

Offset

0,5

Comments

The first 4 occurs at n=2206. The first 5 occurs at n = 361788001015 = A226061(16).

Links

Antti Karttunen, Table of n, a(n) for n = 0..21622

Formula

a(0)=0 and for n>=1, a(n) = A055881(A230406(n)).

For all n, a(A226061(n+1)) = A232096(n).

Mathematica

nn = 1200; m = 1; While[Factorial@ m < nn, m++]; m; t = TakeWhile[
Reverse@ NestList[# - Total@ IntegerDigits[#, MixedRadix[Reverse@ Range[2, m]]] &, nn, 182], # <= 1000 &]; {0}~Join~Table[SelectFirst[Reverse@ Range@ 10, Divisible[t[[n]] - t[[n - 1]], #!] &], {n, 2, 87}] (* Michael De Vlieger, Jun 27 2016, Version 10.2 *)

Prog

(Scheme)
(define (A231719 n) (if (zero? n) n (A055881 (A230406 n))))

Crossrefs

Cf. A055881, A219666, A226061, A230406, A230410, A231717, A232096.

Sequence in context: A318883 A356233 A353382 * A123400 A232502 A288738

Adjacent sequences: A231716 A231717 A231718 * A231720 A231721 A231722

Keyword

nonn

Author

Antti Karttunen, Nov 12 2013

Status

approved