A166574 If p, q are successive primes, and there is a number k with p < k <= q such that r = p+k is a prime, then r is in the sequence.

5, 7, 11, 17, 23, 29, 41, 47, 59, 67, 83, 89, 97, 107, 109, 127, 137, 149, 151, 167, 179, 181, 197, 227, 229, 233, 239, 257, 263, 281, 283, 307, 317, 337, 347, 349, 359, 367, 383, 389, 401, 409, 431, 433, 449, 461, 467, 479, 487, 491

Offset

1,1

Comments

The old definition was: Primes p>=5 with the property: if Prime(k)<p/2<Prime(k+1), then p<=Prime(k)+ Prime(k+1)

If A(x) is the counting function of a(n) not exceeding x, then, in view of the symmetry, it is natural to conjecture that A(x)~pi(x)/2.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

Taking p=2, q=3, k=3 we get r=2+3=5, the first term.
Taking p=3, q=5, k=4 we get r=3+4=7, the second term.
From p=89, q=97 we can take both k=90 and k=92, getting the terms 89+90=179 and 89+92=181. - Art Baker, Mar 16 2019

Mathematica

Reap[Do[p=Prime[n]; k=PrimePi[p/2]; If[p<=Prime[k]+Prime[k+1], Sow[p]], {n, 3, PrimePi[1000]}]][[2, 1]]
Select[#[[1]]+Range[#[[1]]+1, #[[2]]], PrimeQ]&/@Partition[Prime[Range[60]], 2, 1]//Flatten (* Harvey P. Dale, Jul 02 2024 *)

Crossrefs

Cf. A182365, A166307, A166252, A166251, A164368, A104272, A080359, A164333, A164288, A164294, A164554

Sequence in context: A144742 A059786 A300097 * A163846 A354357 A156104

Adjacent sequences: A166571 A166572 A166573 * A166575 A166576 A166577

Keyword

nonn

Author

Vladimir Shevelev, Oct 17 2009

Extensions

Extended by T. D. Noe, Dec 01 2010

Edited with simpler definition based on a suggestion from Art Baker. -N. J. A. Sloane, Mar 16 2019

Status

approved