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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).
2
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
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
KEYWORD
nonn,look
AUTHOR
Vladimir Shevelev, Aug 04 2011
STATUS
approved