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

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, 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, 6, 1, 1, 2, 3, 3, 0, 1, 1, 2, 3, 1, 2, 5, 1, 2, 1, 2, 4

Offset: 0

Author

Arkadiusz Wesolowski, Sep 02 2016

Keywords

• nonn

Comments

a(n) = 1 iff n is in A006254. - Robert Israel, Sep 02 2016

For n > 1, a(n) = 0 iff 2n+1 is de Polignac number, A006285. - Thomas Ordowski, Apr 13 2017

Examples

			a(14) = 4 because (2*14 + 1) - 2^k is composite for k = 1, 2, 3 and prime for k = 4.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A006254, A006285, A101036, A133122, A188903, A232460, A252168.

Programs

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;

Maple

f:= proc(n) local k;
     for k from 1 do
       if 2*n < 2^k then return 0
       elif isprime(2*n+1-2^k) then return k
       fi
     od
end proc:
map(f, [$0..100]); # Robert Israel, Sep 02 2016

Mathematica

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 *)

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

Formula

If A188903(n) >= 2, then a(n) = log_2(A188903(n)), otherwise a(n) = 0.