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

Author

Antti Karttunen, Nov 28 2016

Keywords

• nonn

Examples

			For n=15, we start iterating from the next larger square, (floor(sqrt(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.
		

Links

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

Crossrefs

Cf. A000196, A000290, A002828, A255131.

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

Programs

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)))))))