A209287 - OEIS

%I #30 Mar 18 2019 12:59:48

%S 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,

%T 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,

%U 0,2,0,0,1,2,2,0,0,1,2,2,2,1,3,2,4,2,0

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

%C 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.

%C a(n)=0 if and only if prime(n) is in A074781. - _Robert Israel_, Mar 18 2019

%H Robert Israel, <a href="/A209287/b209287.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%p f:= proc(n) local v,m,p;

%p   p:= ithprime(n)-3;

%p   for m from 0 do

%p     p:= p+2;

%p     v:= p/2^padic:-ordp(p,2);

%p     if v=1 or isprime(v) then return m fi

%p   od;

%p end proc:

%p f(1):= 1:

%p map(f, [$1..100]); # _Robert Israel_, Mar 18 2019

%t 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 *)

%Y Cf. A074781.

%K nonn

%O 1,20

%A _Vladimir Shevelev_, Feb 18 2013

%E More terms from _T. D. Noe_, Feb 26 2013