A346706 Lesser members of twin primes which are the sum of the first k primes for some number k.

5, 17, 41, 197, 281, 38921, 121631, 325019, 642869, 681257, 1005551, 1086557, 2327399, 4975457, 7584569, 7819787, 8130767, 8522159, 14848187, 17769377, 18615677, 19949537, 20144051, 21171191, 24845207, 33669047, 35166449, 56039957, 73479947, 82366769, 92731367

Offset

1,1

Links

Sebastian Sargenti, Table of n, a(n) for n = 1..128

Example

5 = 2+3; 5 is a twin prime with 7.
17 = 2+3+5+7; 17 is a twin prime with 19.
41 = 2+3+5+7+11+13; 41 is a twin prime with 43.
197 = 2+3+5+7+11+13+17+19+23+29+31+37; 197 is a twin prime with 199.

Mathematica

Select[Accumulate @ Select[Range[45000], PrimeQ], PrimeQ[#] && PrimeQ[# + 2] &] (* Amiram Eldar, Aug 01 2021 *)

Prog

(Python)
from itertools import accumulate
from sympy import isprime, primerange
list(filter(lambda p: isprime(p) and isprime(p+2), accumulate(primerange(2, 10000)))) # David Radcliffe, Aug 01 2021
(PARI) lista(nn) = {my(s=0); for (n=1, nn, s += prime(n); if (isprime(s) && isprime(s+2), print1(s, ", ")); ); } \\ Michel Marcus, Aug 21 2021

Crossrefs

Cf. A000040, A007504.

Intersection of A001359 and A013918.

Sequence in context: A273116 A273945 A111268 * A106973 A102264 A122035

Adjacent sequences: A346703 A346704 A346705 * A346707 A346708 A346709

Keyword

nonn

Author

Sebastian Sargenti, Jul 29 2021

Extensions

a(13)-a(31) from Jon E. Schoenfield, Jul 29 2021

Status

approved