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%I #15 Apr 19 2015 00:53:12
%S 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,
%T 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,
%U 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
%N One-based column index of n in array A255555.
%C Equally: One-based row index of n in array A255557.
%H Antti Karttunen, <a href="/A255559/b255559.txt">Table of n, a(n) for n = 1..8192</a>
%F 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).
%F 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.
%F Other identities and observations. For all n >= 1:
%F a(n) <= A256478(n) <= A070939(n).
%F a(n) <= A256993(n) + 1.
%o (Scheme, with memoization-macro definec)
%o (definec (A255559 n) (if (or (= 1 n) (zero? (A213714 n))) 1 (+ 1 (A255559 (+ -1 (A213714 n))))))
%Y Cf. A005187, A055938, A070939, A213714, A255555, A255557.
%Y Cf. also A255560 (corresponding row index).
%Y Cf. A254111, A256989, A256478, A256993.
%K nonn
%O 1,3
%A _Antti Karttunen_, Apr 14 2015
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