A256989 - OEIS

%I #12 Apr 19 2015 00:53:36

%S 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,

%T 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,

%U 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

%N One-based column index of n in array A256995.

%C Also one-based row index for array A256997.

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

%H Antti Karttunen, <a href="/A256989/b256989.txt">Table of n, a(n) for n = 1..8192</a>

%F 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)).

%F 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.

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

%F a(n) <= A256993(n).

%o (Scheme, with memoization-macro definec)

%o (definec (A256989 n) (cond ((= 1 n) 0) ((zero? (A213714 n)) 1) (else (+ 1 (A256989 (A213714 n))))))

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

%Y Cf. A256990 (corresponding row index), A255559.

%K nonn

%O 1,3

%A _Antti Karttunen_, Apr 14 2015