A357122 Numbers k such that the sum of (q mod p) for pairs of primes p<q such that p+q=2*k is prime.

4, 6, 7, 8, 9, 11, 13, 19, 24, 29, 31, 34, 39, 41, 44, 52, 59, 69, 73, 74, 81, 84, 96, 97, 102, 103, 107, 108, 113, 115, 118, 119, 120, 129, 135, 145, 153, 160, 164, 182, 207, 212, 230, 236, 243, 261, 264, 277, 285, 299, 306, 329, 337, 340, 342, 347, 358, 379, 386, 397, 410, 415, 420, 428, 434

Offset

1,1

Comments

Numbers k such that A338984(k) is prime.

Links

Robert Israel, Table of n, a(n) for n = 1..2000

Example

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.

Maple

N:= 2000: # for terms <= N/2
P:= select(isprime, [seq(i, i=3..N, 2)]):
nP:= nops(P):
V:= Vector(N):
for i from 1 to nP do
  for j from i+1 to nP do
    v:= P[i]+P[j];
    if v > N then break fi;
    V[v]:= V[v] + (P[j] mod P[i])
od od:
select(t -> isprime(V[2*t]), [$1..N/2]);

Crossrefs

Cf. A338984.

Sequence in context: A114308 A299411 A079000 * A047509 A181057 A151757

Adjacent sequences: A357119 A357120 A357121 * A357123 A357124 A357125

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Sep 12 2022

Status

approved