



0, 1, 2, 2, 3, 3, 3, 3, 1, 6, 3, 3, 3, 2, 1, 6, 2, 3, 1, 3, 5, 3, 1, 3, 6, 2, 2, 3, 10, 3, 3, 3, 2, 1, 6, 2, 3, 1, 3, 5, 3, 1, 3, 6, 2, 1, 3, 5, 5, 3, 10, 2, 3, 1, 3, 5, 3, 1, 3, 6, 2, 1, 2, 4, 2, 4, 5, 3, 3, 9, 3, 1, 3, 6, 2, 1, 2, 4, 2, 4, 5, 3, 2, 4, 3, 10
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OFFSET

0,3


COMMENTS

For all n, a(A226061(n+1)) = A232095(n). This works because at the positions given by each x=A226061(n+1), it holds that A219666(x) = (n+1)!1, which has a factorial base representation (A007623) of (n,n1,n2,...,3,2,1) whose digit sum (A034968) is the nth triangular number, A000217(n). This in turn is always a new record as at those points, in each significant digit position so far employed, a maximal digit value (for factorial number system) is used, and thus the preceding term, A219666(x1) cannot have any larger digits in its factorial base representation, and so the differences between their digits (in matching positions) are all nonnegative.


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..3149


FORMULA

a(0)=0, and for n>=1, a(n) = A231713(A219666(n),A219666(n1)).


PROG

(Scheme)
(define (A231717 n) (if (zero? n) n (A231713bi (A219666 n) (A219666 ( n 1)))))


CROSSREFS

A231718 gives the positions of ones.
Cf. also A230410, A231719, A232095.
Sequence in context: A260236 A122462 A215406 * A253315 A210480 A321859
Adjacent sequences: A231714 A231715 A231716 * A231718 A231719 A231720


KEYWORD

nonn


AUTHOR

Antti Karttunen, Nov 12 2013


STATUS

approved



