A335969 Sphenic numbers that are also the sum of three consecutive primes.

1015, 1533, 1645, 2233, 2737, 2915, 3219, 3515, 3745, 3815, 4301, 4503, 4565, 4623, 4697, 4921, 5289, 5621, 6055, 6095, 6213, 6251, 6409, 7055, 7347, 7657, 7847, 8099, 8455, 8569, 8687, 8729, 9499, 9581, 9955, 10105, 10153, 10295, 10735, 11155, 11297, 11315, 11803, 12665, 12805, 12845

Offset: 1

Author

Zak Seidov, Jul 04 2020

Keywords

• nonn

Comments

Intersection of A007304 and A034961.

Includes 15*p where p, 5*p-14, 5*p-2 and 5*p+16 are consecutive primes. Dickson's conjecture implies there are infinitely many such terms. - Robert Israel, Nov 24 2022

Examples

			1015 = A007304(140) = A034961(67), 1533 = A007304(226) = A034961(96).
		

Links

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

Crossrefs

Cf. A007304, A034961.

Programs

Maple

P:= select(isprime, [seq(i,i=3..10^4,2)]):
P3:= P[1..-3] + P[2..-2] + P[3..-1]:
filter:= proc(t) local F; F:= ifactors(t)[2]; nops(F) = 3 and F[1,2]=1 and F[2,2] = 1 and F[3,2]=1 end proc:
select(filter, P3); # Robert Israel, Nov 24 2022

Mathematica

Intersection[ Select[Range[105, 40000,2], 3 == PrimeOmega[#] == PrimeNu[#] &], Total /@ Partition[Prime[Range[40000]], 3, 1]]