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

1,1

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

Links

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

Example

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

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]]

Crossrefs

Cf. A007304, A034961.

Sequence in context: A234754 A023076 A261291 * A225717 A117807 A223089

Adjacent sequences: A335966 A335967 A335968 * A335970 A335971 A335972

Keyword

nonn

Author

Zak Seidov, Jul 04 2020

Status

approved