A209287 Minimal m>=0 such that prime(n)+2*m-1 has form 2^k*p, where k>=0 and p is prime.

1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 2, 1, 0, 2, 0, 1, 2, 0, 2, 0, 1, 1, 1, 0, 0, 0, 2, 1, 0, 3, 2, 1, 1, 0, 2, 0, 3, 2, 2, 0, 0, 0, 1, 1, 2, 1, 0, 4, 2, 1, 0, 1, 4, 0, 2, 0, 0, 1, 2, 2, 0, 0, 1, 2, 2, 2, 1, 3, 2, 4, 2, 0

Offset: 1

Author

Vladimir Shevelev, Feb 18 2013

Keywords

• nonn

Comments

Or, for n>2, a(n) is the minimal m>=0 such that the divided on prime(n) sum of prime(n) consecutive integers beginning with m has form 2^k*p, where k>=0 and p is prime.

a(n)=0 if and only if prime(n) is in A074781. - Robert Israel, Mar 18 2019

Examples

			Let n=7. Then prime(7)=17 and, for m=0, 17+2m-1=16=2^3*p, where p=2. Thus a(7)=0.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A074781.

Programs

Maple

f:= proc(n) local v,m,p;
  p:= ithprime(n)-3;
  for m from 0 do
    p:= p+2;
    v:= p/2^padic:-ordp(p,2);
    if v=1 or isprime(v) then return m fi
  od;
end proc:
f(1):= 1:
map(f, [$1..100]); # Robert Israel, Mar 18 2019

Mathematica

good[n_] := Module[{k = n/2^IntegerExponent[n, 2]}, n > 1 && (k == 1 || PrimeQ[k])]; Table[p = Prime[n]; m = 0; While[! good[p + 2*m - 1], m++]; m, {n, 87}] (* T. D. Noe, Feb 26 2013 *)

Extensions

More terms from T. D. Noe, Feb 26 2013