A350694 Numbers that can be written as p*q+r where p,q,r are primes (not necessarily distinct) such that p+q+r is prime.

7, 8, 11, 14, 16, 17, 18, 20, 22, 23, 24, 26, 28, 32, 34, 36, 38, 40, 41, 42, 44, 46, 47, 50, 52, 54, 56, 58, 62, 64, 66, 68, 70, 71, 72, 74, 76, 78, 80, 82, 83, 84, 86, 88, 90, 92, 94, 96, 98, 100, 101, 102, 104, 106, 107, 108, 110, 112, 113, 114, 116, 118, 120, 122, 124, 126, 128, 130, 131, 132

Offset

1,1

Comments

Conjecture: the sequence contains all even positive integers except 2, 4, 6, 10, 12, 30, 48, 60.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(4) = 14 is a term because 14 = 3*3+5 where 3+3+5 = 11 is prime.

Maple

N:= 500: # for terms <= N
P:= select(isprime, [2, seq(i, i=3..N, 2)]):
PS:= convert(P, set):
nP:= nops(P):
S:= {}:
for i from 1 to nP do
  for j from i to nP while P[i]*P[j] < N do
    S:= S union select(`<=`, map(`+`, PS intersect map(`-`, PS, P[i]+P[j]), P[i]*P[j]), N)
od od:
sort(convert(S, list));

Crossrefs

Odd terms are A046132.

Sequence in context: A277026 A309592 A090385 * A145826 A102963 A117619

Adjacent sequences: A350691 A350692 A350693 * A350695 A350696 A350697

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jan 28 2022

Status

approved