A280536 Numbers n such that the sum of the first n primes reduced by some power of 2 is prime.

2, 3, 4, 5, 6, 7, 11, 12, 14, 15, 19, 21, 27, 35, 55, 59, 60, 64, 65, 75, 81, 83, 93, 95, 96, 100, 102, 108, 109, 114, 122, 124, 130, 132, 133, 135, 137, 141, 146, 152, 155, 158, 162, 165, 171, 178, 183, 192, 193, 198, 204, 206, 208, 214, 216, 223, 227, 243, 249, 255, 257, 263, 277, 279, 296

Offset

1,1

Comments

A013916 except for the first term, 1, is a proper subset.

The odd terms are: 3, 5, 7, 11, 15, 19, 21, 27, 35, 55, 59, 65, 75, 81, 83, ..., .

The 10^k-th term: 2, 15, 469, 7980, 110374, 1359497, 16214466, 187663922, ..., .

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Example

11 is in the sequence since the sum of the first 11 primes is A007504(11) = 160 and 160 is divisible by 2^5 which gives 5, a prime.

Mathematica

fQ[n_] := Block[{s = Sum[ Prime@ k, {k, n}]}, PrimeQ[s/2^IntegerExponent[s, 2]]]; Select[Range@300, fQ]

Crossrefs

Cf. A007504, A013916.

Sequence in context: A032976 A174219 A115037 * A090563 A045745 A054010

Adjacent sequences: A280533 A280534 A280535 * A280537 A280538 A280539

Keyword

nonn

Author

Robert G. Wilson v, Jan 04 2017

Status

approved