A338083 Primes p such that p+2 is prime and the sum of prime factors of p+1 (taken with repetition) is prime.

5, 11, 107, 197, 419, 431, 461, 521, 569, 599, 659, 809, 857, 1019, 1061, 1277, 1289, 1301, 1427, 1451, 1481, 1721, 1931, 2087, 2267, 3119, 3467, 3539, 4019, 4157, 4217, 4241, 4259, 4421, 5279, 5639, 5651, 5849, 5867, 6359, 6689, 6869, 7127, 7331, 7349, 7487, 7547, 7757, 8219, 8819, 8837, 8861

Offset

1,1

Links

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

Example

a(3)=107 is a term because 107 and 109 are prime while 108=2^2*3^3 and 2*2+3*3=13 is prime.

Maple

TP:= select(t -> isprime(t) and isprime(t+2), [seq(i, i=5..1000, 6)]):
select(p -> isprime(add(t[1]*t[2], t=ifactors(p+1)[2])), TP);

Mathematica

Select[Partition[Prime[Range[1250]], 2, 1], #[[2]]-#[[1]]==2&&PrimeQ[Total[ Times@@@ FactorInteger[#[[1]]+1]]]&][[All, 1]] (* Harvey P. Dale, Jul 10 2022 *)

Crossrefs

Intersection of A001359 and A127269.

Sequence in context: A090160 A062652 A075706 * A236509 A330488 A057178

Adjacent sequences: A338080 A338081 A338082 * A338084 A338085 A338086

Keyword

nonn

Author

Robert Israel, Oct 08 2020

Status

approved