

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.


1



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
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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

Table of n, a(n) for n=1..50.


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]]


CROSSREFS

Cf. A166308, A166307, A166252, A166251, A164368, A104272, A080359, A164333, A164288, A164294, A164554
Sequence in context: A144742 A059786 A300097 * A163846 A156104 A191080
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



