A278515 Number of steps required to iterate map k -> A255131(k) when starting from k = (A000196(n)+1)^2 before n is reached, or 0 if n is not reached.

1, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 2, 0, 0, 0, 1, 4, 0, 3, 0, 0, 2, 0, 0, 1, 0, 0, 4, 0, 0, 3, 0, 2, 0, 0, 1, 0, 0, 5, 0, 4, 0, 0, 3, 0, 2, 0, 0, 1, 0, 0, 5, 0, 4, 0, 0, 3, 0, 0, 2, 0, 0, 0, 1, 7, 0, 0, 6, 0, 0, 5, 0, 4, 0, 0, 3, 0, 0, 2, 0, 1, 0, 0, 7, 0, 6, 0, 0, 5, 0, 4, 0, 0, 3, 0, 0, 2, 0, 0, 1, 0, 0, 7, 0, 0, 6, 0, 0, 5, 0, 0, 0, 4, 0, 0, 3, 0, 2, 0, 0, 1

Offset

0,7

Links

Antti Karttunen, Table of n, a(n) for n = 0..10200

Example

For n=15, we start iterating from the next larger square, (⌊√15⌋+1)^2 = 16, and in just a single step (16 - A002828(16) = 15) we land to n, so a(15) = 1.
For n=16, we start iterating from the next larger square, which is 25, and thus we have 25 -> A255131(25) = 24, 24 -> A255131(24) = 21, 21 -> A255131(21) = 18, 18 -> A255131(18) = 16, thus four steps were required to reach 16, and a(16) = 4.
For n=17, when we do the same iteration, we see that we will pass by it, thus a(17) = 0.

Prog

(Scheme) (define (A278515 n) (let* ((r (A000196 n)) (end (A000290 r))) (let loop ((k (A000290 (+ 1 r))) (s 0)) (cond ((= k n) s) ((<= k end) 0) (else (loop (A255131 k) (+ 1 s)))))))

Crossrefs

Cf. A000196, A000290, A002828, A255131.

Cf. A005563 (positions of ones), A276573 (of nonzero terms).

Sequence in context: A226861 A185643 A363051 * A285709 A080101 A025895

Adjacent sequences: A278512 A278513 A278514 * A278516 A278517 A278518

Keyword

nonn

Author

Antti Karttunen, Nov 28 2016

Status

approved