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A155891 Least positive integer such that a(n)! starts with n, both written in binary.

%I A155891 #14 Mar 05 2024 02:44:39
%S A155891 1,2,3,7,6,3,5,20,7,14,6,4,10,12,5,20,27,50,7,14,23,6,13,4,25,30,10,
%T A155891 12,51,5,63,24,20,36,27,50,59,11,7,14,26,75,23,9,6,13,49,71,144,31,25,
%U A155891 30,199,19,10,46,12,51,83,5,28,73,63,62,24,54,20,36,67,27,40,74,50,59,124
%N A155891 Least positive integer such that a(n)! starts with n, both written in binary.
%H A155891 Nick Hobson, <a href="/A155891/b155891.txt">Table of n, a(n) for n = 1..16383</a>
%H A155891 Nick Hobson, <a href="/A155891/a155891_1.c.txt">C program</a>.
%e A155891 a(7) = 5 since 7 = 111_2 (i.e., written in base 2) and 5! = 1111000_2 is the least factorial to have 111 as its most significant binary digits.
%o A155891 (PARI) A155891(n)={ local( F=1,k=1 ); while( F\1!=n, F*=k++; while( F>=n+1, F/=2 )); k}
%o A155891 (C) See Links section.
%Y A155891 Cf. A018799, A076219.
%K A155891 base,nonn
%O A155891 1,2
%A A155891 _M. F. Hasler_, Feb 01 2009