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A105888 a(n) = the smallest prime that, when written in binary, ends with the substring of 2n-1 in binary.

%I A105888 #14 Feb 05 2020 14:28:12
%S A105888 3,3,5,7,41,11,13,31,17,19,53,23,89,59,29,31,97,163,37,103,41,43,109,
%T A105888 47,113,179,53,311,313,59,61,127,193,67,197,71,73,331,461,79,337,83,
%U A105888 853,599,89,347,349,223,97,227,101,103,233,107,109,239,113,499,373,503,761
%N A105888 a(n) = the smallest prime that, when written in binary, ends with the substring of 2n-1 in binary.
%H A105888 Rémy Sigrist, <a href="/A105888/b105888.txt">Table of n, a(n) for n = 1..8192</a>
%e A105888 2*5-1 = 9 is 1001 in binary. Looking at the binary numbers that end with 1001: 1001 = 9 in decimal is composite; 11001 = 25 in decimal is composite. But 101001 = 41 in decimal is prime. So a(5) = 41. - Corrected by _Rémy Sigrist_, Feb 05 2020
%p A105888 isA105888 := proc(p,n) local pdgs,n21dgs ; pdgs := convert(p,base,2) ; n21dgs := convert(2*n-1,base,2) ; if nops(n21dgs) > nops(pdgs) then return false; else verify( [op(1..nops(n21dgs),n21dgs)],[op(1..nops(n21dgs),pdgs)],'sublist') ; end if; end proc: A105888 := proc(n) p := 2 ; while not isA105888(p,n) do p := nextprime(p) ; end do ; p ; end proc: seq(A105888(n),n=1..80) ; # _R. J. Mathar_, Dec 06 2009
%t A105888 pr=-16; Select[Prime[Range[200]], MultiplicativeOrder[pr, # ] == #-1 &]
%o A105888 (PARI) a(n) = my (m=2*n-1); forstep (p=m, oo, 2^#binary(m), if (isprime(p), return (p)))
%Y A105888 Cf. A164022.
%K A105888 base,nonn
%O A105888 1,1
%A A105888 _Leroy Quet_, Aug 08 2009
%E A105888 Extended beyond a(10) by _R. J. Mathar_, Dec 06 2009