A366206 Numbers k such that the sum of the first k primes is the average of a twin prime pair.

57, 103, 123, 211, 213, 273, 347, 943, 1073, 1951, 2185, 2365, 2375, 2379, 2501, 2751, 2761, 2855, 3095, 3651, 3731, 3791, 3799, 4503, 4529, 4843, 5199, 5851, 5927, 5959, 6163, 7151, 7305, 7611, 8101, 8761, 9045, 9061, 9429, 9497, 9741, 9909, 10071, 10105, 10401

Offset

1,1

Comments

All terms are odd. - Karl-Heinz Hofmann, Sep 15 2025

Links

Paolo Xausa, Table of n, a(n) for n = 1..5000

Mathematica

With[{upto=10^4}, Flatten[Position[Accumulate[Prime[Range[upto]]], _?(PrimeQ[#-1]&&PrimeQ[#+1]&)]]]

Prog

(PARI) isok(k) = my(s=vecsum(primes(k))); isprime(s-1) && isprime(s+1); \\ Michel Marcus, Oct 04 2023
(Python)
from sympy import isprime, sieve
print([k for k in range(1, 10402, 2) if isprime((s:=sum(sieve[1:k+1]))-1) and isprime(s+1)])
# Karl-Heinz Hofmann, Sep 15 2025

Crossrefs

Cf. A007504, A014574, A366205 (corresponding sums).

Sequence in context: A147468 A147036 A147044 * A237663 A039535 A037990

Adjacent sequences: A366203 A366204 A366205 * A366207 A366208 A366209

Keyword

nonn

Author

Paolo Xausa, Oct 04 2023

Status

approved