A193262 Number of representations of 2*p_n as sum of two primes p,q such that p*q-2 is prime (p_n is the n-th prime).

1, 1, 2, 2, 1, 3, 1, 1, 2, 2, 0, 3, 0, 2, 3, 4, 2, 1, 3, 4, 2, 0, 4, 2, 5, 2, 2, 5, 2, 2, 5, 2, 4, 1, 0, 1, 2, 0, 8, 3, 0, 2, 2, 5, 3, 0, 1, 5, 7, 1, 3, 1, 2, 4, 5, 5, 1, 0, 3, 2, 4, 3, 4, 2, 3, 3, 1, 3, 2, 0, 8, 3, 4, 3, 0, 9, 1, 6, 0, 2, 5, 2, 2, 9, 1, 5, 4, 3, 1, 7, 5, 2, 4, 2, 1

Offset

1,3

Comments

Sequence arising in connection with conjecture in comment to A192189.

Conjecture: There exists n_0, such that, for n>n_0, a(n)>0.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Example

a(4)=2 since 2*p(4) = 14 = 3+11 = 7+7, and 3*11-2 = 31, 7*7-2 = 47 are prime.

Maple

a:= proc(n) local t, s, p, q;
      t:= 2*ithprime(n);
      s:= 0;
      p:= 2;
      do q:= t-p;
         if q<p then break fi;
         if isprime(q) and isprime(p*q-2) then s:= s+1 fi;
         p:= nextprime(p)
      od; s
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 04 2011

Mathematica

a[n_] := Module[{t = 2 Prime[n], s = 0, p = 2, q}, While[True, q = t - p; If[q < p, Break[]]; If[PrimeQ[q] && PrimeQ[p q - 2], s++]; p = NextPrime[p]]; s];
Array[a, 100] (* Jean-François Alcover, Nov 11 2020, after Alois P. Heinz *)

Prog

(PARI) A193262(n, c=0)={ n=2*prime(n); forprime(p=1, n/2, isprime(n-p) || next; isprime(p*(n-p)-2) & c++); c}  \\ M. F. Hasler, Aug 06 2011

Crossrefs

Cf. A045917.

Sequence in context: A077889 A305805 A230260 * A120967 A116687 A264033

Adjacent sequences: A193259 A193260 A193261 * A193263 A193264 A193265

Keyword

nonn,look

Author

Vladimir Shevelev, Aug 04 2011

Status

approved