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A236837 The greatest inverse of A234741: a(n) = the largest k such that A234741(k) = n, and 0 if no such k exists.

%I A236837 #11 Feb 07 2014 10:45:09
%S A236837 0,1,2,3,4,9,6,7,8,21,18,11,12,13,14,27,16,81,42,19,36,49,22,39,24,0,
%T A236837 26,63,28,33,54,31,32,93,162,91,84,37,38,99,72,41,98,43,44,189,78,47,
%U A236837 48,77,0,243,52,57,126,0,56,117,66,59,108,61,62,147,64,441,186,67,324,121
%N A236837 The greatest inverse of A234741: a(n) = the largest k such that A234741(k) = n, and 0 if no such k exists.
%C A236837 A234741(a(n)) = n, unless n is in A236834, in which case a(n)=0.
%C A236837 For all n, a(n) <= A234742(n). A236850 gives such k that a(k) = A234742(k).
%C A236837 If n is in A236835, a(n) > A236836(n), otherwise a(n) = A236836(n).
%C A236837 a(2^n) = 2^n.
%C A236837 a(2n) = 2*a(n).
%H A236837 Antti Karttunen, <a href="/A236837/b236837.txt">Table of n, a(n) for n = 0..8192</a>
%o A236837 (Scheme, finding the greatest inverse empirically with a naive loop. A234742 gives an absolute upper bound for any inverse of A234741):
%o A236837 (define (A236837 n) (let ((u (A234742 n))) (let loop ((i u)) (let ((k (A234741 i))) (cond ((< i n) 0) ((= k n) i) (else (loop (- i 1))))))))
%Y A236837 A236834 gives the positions of zeros.
%Y A236837 Differs from A235042 and A234742 for the first time at n=25, where a(25)=0 but A235042(25)=5 and A234742(25)=25.
%Y A236837 Cf. A236836 (the least inverse of A234741).
%Y A236837 Cf. also A236833, A236835, A234741, A236841, A236850.
%K A236837 nonn
%O A236837 0,3
%A A236837 _Antti Karttunen_, Jan 31 2014