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Numbers k such that the sum of (q mod p) for pairs of primes p<q such that p+q=2*k is prime.
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%I #9 Oct 02 2022 13:29:33

%S 4,6,7,8,9,11,13,19,24,29,31,34,39,41,44,52,59,69,73,74,81,84,96,97,

%T 102,103,107,108,113,115,118,119,120,129,135,145,153,160,164,182,207,

%U 212,230,236,243,261,264,277,285,299,306,329,337,340,342,347,358,379,386,397,410,415,420,428,434

%N Numbers k such that the sum of (q mod p) for pairs of primes p<q such that p+q=2*k is prime.

%C Numbers k such that A338984(k) is prime.

%H Robert Israel, <a href="/A357122/b357122.txt">Table of n, a(n) for n = 1..2000</a>

%e a(5) = 9 is a term because 2*9 = 5 + 13 = 7 + 11 with (13 mod 5) + (11 mod 7) = 3 + 4 = 7. which is prime.

%p N:= 2000: # for terms <= N/2

%p P:= select(isprime, [seq(i, i=3..N, 2)]):

%p nP:= nops(P):

%p V:= Vector(N):

%p for i from 1 to nP do

%p for j from i+1 to nP do

%p v:= P[i]+P[j];

%p if v > N then break fi;

%p V[v]:= V[v] + (P[j] mod P[i])

%p od od:

%p select(t -> isprime(V[2*t]), [$1..N/2]);

%Y Cf. A338984.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Sep 12 2022