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A335969
Sphenic numbers that are also the sum of three consecutive primes.
1
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
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
Sequence in context: A234754 A023076 A261291 * A225717 A117807 A223089
KEYWORD
nonn
AUTHOR
Zak Seidov, Jul 04 2020
STATUS
approved