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A276417 a(n) = least positive k such that (2*n + 1) - 2^k is prime, or 0 if no such k exists.

%I A276417 #24 Sep 08 2022 08:46:17
%S A276417 0,0,1,1,1,2,1,1,2,1,1,2,1,2,4,1,1,2,3,1,2,1,1,2,1,2,4,1,2,4,1,1,2,3,
%T A276417 1,2,1,1,2,3,1,2,1,2,4,1,2,4,3,1,2,1,1,2,1,1,2,1,2,4,3,4,4,0,1,2,1,2,
%U A276417 6,1,1,2,3,3,0,1,1,2,3,1,2,5,1,2,1,2,4
%N A276417 a(n) = least positive k such that (2*n + 1) - 2^k is prime, or 0 if no such k exists.
%C A276417 a(n) = 1 iff n is in A006254. - _Robert Israel_, Sep 02 2016
%C A276417 For n > 1, a(n) = 0 iff 2n+1 is de Polignac number, A006285. - _Thomas Ordowski_, Apr 13 2017
%H A276417 Robert Israel, <a href="/A276417/b276417.txt">Table of n, a(n) for n = 0..10000</a>
%F A276417 If A188903(n) >= 2, then a(n) = log_2(A188903(n)), otherwise a(n) = 0.
%e A276417 a(14) = 4 because (2*14 + 1) - 2^k is composite for k = 1, 2, 3 and prime for k = 4.
%p A276417 f:= proc(n) local k;
%p A276417      for k from 1 do
%p A276417        if 2*n < 2^k then return 0
%p A276417        elif isprime(2*n+1-2^k) then return k
%p A276417        fi
%p A276417      od
%p A276417 end proc:
%p A276417 map(f, [$0..100]); # _Robert Israel_, Sep 02 2016
%t A276417 Table[If[n <= 2, 0, k = 1; While[! PrimeQ[2 n + 1 - 2^k], k++]; k], {n, 0, 120}] (* _Michael De Vlieger_, Sep 03 2016 *)
%o A276417 (Magma) lst:=[]; for n in [1..173 by 2] do k:=0; c:=k; repeat k+:=1; c+:=1; a:=n-2^k; until a lt 1 or IsPrime(a); if a lt 1 then Append(~lst, 0); else Append(~lst, c); end if; end for; lst;
%o A276417 (PARI) a(n) = my(k=1); while(2^k < 2*n+1, if(ispseudoprime((2*n+1)-2^k), return(k)); k++); return(0) \\ _Felix Fröhlich_, Sep 02 2016
%Y A276417 Cf. A006254, A006285, A101036, A133122, A188903, A232460, A252168.
%K A276417 nonn
%O A276417 0,6
%A A276417 _Arkadiusz Wesolowski_, Sep 02 2016