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a(n) is the number of primes of the form prime(n) + 2*q where q < prime(n) is prime.
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%I #12 May 16 2023 10:39:54

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

%T 7,10,11,8,8,9,8,9,8,10,7,9,11,14,10,13,11,9,12,13,10,12,12,13,12,10,

%U 15,15,17,15,12,12,12,15,15,17,17,11,16,16,17,17,13,19,14,17,14,17,12,15,19

%N a(n) is the number of primes of the form prime(n) + 2*q where q < prime(n) is prime.

%H Robert Israel, <a href="/A344793/b344793.txt">Table of n, a(n) for n = 1..5000</a>

%e a(6) = 3 because with prime(6) = 13 we have 2*2+13 = 17, 2*3+13 = 19 and 2*5+13 = 23 prime.

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

%p p:= ithprime(n);

%p numboccur(true,map(isprime, [seq(2*ithprime(i)+p,i=1..n-1)]))

%p end proc:

%p map(f, [$1..100]);

%t a[n_] := Module[{p, q},

%t p = Prime[n];

%t q = Select[Range[p-1], PrimeQ];

%t Count[p + 2 q, _?PrimeQ]];

%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, May 16 2023 *)

%Y Cf. A344794.

%K nonn

%O 1,4

%A _J. M. Bergot_ and _Robert Israel_, May 28 2021