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

Author

Paolo Xausa, Oct 04 2023

Keywords

• nonn

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

isok(k) = my(s=vecsum(primes(k))); isprime(s-1) && isprime(s+1); \\ Michel Marcus, Oct 04 2023