A255559 One-based column index of n in array A255555.

1, 1, 2, 2, 1, 1, 3, 3, 1, 2, 2, 1, 1, 1, 4, 4, 1, 2, 3, 1, 1, 3, 2, 1, 2, 2, 1, 1, 1, 1, 5, 5, 1, 2, 3, 1, 1, 4, 2, 1, 2, 4, 1, 1, 1, 3, 2, 1, 3, 3, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 1, 1, 6, 6, 1, 2, 3, 1, 1, 4, 2, 1, 2, 5, 1, 1, 1, 3, 2, 1, 3, 5, 1, 1, 2, 2, 1, 2, 4, 1, 1, 1, 1, 3, 2, 1, 4, 4, 1, 1, 2, 2, 1, 3, 3, 1

Offset

1,3

Comments

Equally: One-based row index of n in array A255557.

Links

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

Formula

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

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

Other identities and observations. For all n >= 1:

a(n) <= A256478(n) <= A070939(n).

a(n) <= A256993(n) + 1.

Prog

(Scheme, with memoization-macro definec)
(definec (A255559 n) (if (or (= 1 n) (zero? (A213714 n))) 1 (+ 1 (A255559 (+ -1 (A213714 n))))))

Crossrefs

Cf. A005187, A055938, A070939, A213714, A255555, A255557.

Cf. also A255560 (corresponding row index).

Cf. A254111, A256989, A256478, A256993.

Sequence in context: A037162 A352911 A278566 * A181935 A027358 A332548

Adjacent sequences: A255556 A255557 A255558 * A255560 A255561 A255562

Keyword

nonn

Author

Antti Karttunen, Apr 14 2015

Status

approved