%I #11 Mar 08 2014 08:52:42

%S 0,1,2,3,4,0,6,7,8,5,0,11,12,13,14,0,16,0,10,19,0,9,22,0,24,25,26,15,

%T 28,0,0,31,32,29,0,0,20,37,38,23,0,41,18,0,44,0,0,47,48,21,50,0,52,0,

%U 30,55,56,53,0,59,0,61,62,27,64,0,58,67,0,0,0,0,40,73,74,43,76,49,46,0,0,17,82,0,36,0,0,87,88,0,0,35

%N Least inverse of A234742: a(n) = minimal k such that when it is remultiplied "upwards", from GF(2)[X] to N, the result is n, and 0 if no such k exists.

%C Apart from zero, each term occurs at most once. 91 is the smallest positive integer not present in this sequence.

%C Note that in contrast to the reciprocal case, where A234742(n) >= A236837(n) for all n [the former sequence gives the absolute upper bound for the latter], here it is not guaranteed that A234741(n) <= a(n) whenever a(n) > 0. For example, a(25)=25 and A234741(25)=17, and 25-17 = 8. On the other hand, a(75)=43, but A234741(75)=51, and 43-51 = -8.

%H Antti Karttunen, <a href="/A236846/b236846.txt">Table of n, a(n) for n = 0..8192</a>

%F a(n) = minimal k such that A234742(k) = n, and 0 if no such k exists.

%F For all n, a(n) <= n.

%o (Scheme) (define (A236846 n) (let loop ((k n) (minv 0)) (cond ((zero? k) minv) ((= (A234742 k) n) (loop (- k 1) k)) (else (loop (- k 1) minv)))))

%Y Differs from A236847 for the first time at n=91, where a(91)=35, while A236847(91)=91.

%Y A236844 gives the positions of zeros.

%Y Cf. A234742.

%Y Cf. also A236836, A236837.

%K nonn

%O 0,3

%A _Antti Karttunen_, Jan 31 2014