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

%I A256989 #12 Apr 19 2015 00:53:36
%S A256989 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 A256989 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 A256989 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 A256989 One-based column index of n in array A256995.
%C A256989 Also one-based row index for array A256997.
%C A256989 a(1) = 0 by convention, as 1 is outside of the actual arrays A256995 & A256997.
%H A256989 Antti Karttunen, <a href="/A256989/b256989.txt">Table of n, a(n) for n = 1..8192</a>
%F A256989 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 A256989 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 A256989 Other observations. For all n >= 1 it holds that:
%F A256989 a(n) <= A256993(n).
%o A256989 (Scheme, with memoization-macro definec)
%o A256989 (definec (A256989 n) (cond ((= 1 n) 0) ((zero? (A213714 n)) 1) (else (+ 1 (A256989 (A213714 n))))))
%Y A256989 Cf. A005187, A055938, A213714, A256995, A256997.
%Y A256989 Cf. A256990 (corresponding row index), A255559.
%K A256989 nonn
%O A256989 1,3
%A A256989 _Antti Karttunen_, Apr 14 2015