A256989 One-based column index of n in array A256995.

0, 1, 2, 3, 1, 1, 4, 2, 1, 2, 5, 1, 1, 1, 3, 2, 1, 3, 6, 1, 1, 2, 2, 1, 2, 4, 1, 1, 1, 1, 3, 2, 1, 4, 7, 1, 1, 2, 2, 1, 3, 3, 1, 1, 1, 2, 3, 1, 5, 2, 1, 1, 2, 2, 1, 2, 4, 1, 1, 1, 1, 1, 3, 2, 1, 5, 8, 1, 1, 2, 2, 1, 3, 3, 1, 1, 1, 2, 4, 1, 4, 2, 1, 1, 2, 2, 1, 3, 4, 1, 1, 1, 1, 2, 6, 1, 3, 2, 1, 1, 2, 3, 1, 3, 2, 1, 1, 1, 3, 5, 1, 2, 2, 1, 1, 2, 2, 1, 2, 4

Offset

1,3

Comments

Also one-based row index for array A256997.

a(1) = 0 by convention, as 1 is outside of the actual arrays A256995 & A256997.

Links

Antti Karttunen, Table of n, a(n) for n = 1..8192

Formula

a(1) = 0; for n > 1, if A213714(n) = 0 [i.e., if n is one of the terms of A055938], then a(n) = 1, otherwise a(n) = 1 + a(A213714(n)).

In other words, a(1) = 0, and for n > 1, if n = A005187(k) for some k, then a(n) = 1 + a(k), otherwise it must be that n is in A055938, in which case a(n) = 1.

Other observations. For all n >= 1 it holds that:

a(n) <= A256993(n).

Prog

(Scheme, with memoization-macro definec)
(definec (A256989 n) (cond ((= 1 n) 0) ((zero? (A213714 n)) 1) (else (+ 1 (A256989 (A213714 n))))))

Crossrefs

Cf. A005187, A055938, A213714, A256995, A256997.

Cf. A256990 (corresponding row index), A255559.

Sequence in context: A194518 A023572 A023570 * A275214 A319846 A214690

Adjacent sequences: A256986 A256987 A256988 * A256990 A256991 A256992

Keyword

nonn

Author

Antti Karttunen, Apr 14 2015

Status

approved