A166575 Primes p>=5 with the property: if Prime(k)<p/2<Prime(k+1), then p>=Prime(k)+ Prime(k+1)

5, 13, 19, 31, 37, 43, 53, 61, 71, 73, 79, 101, 103, 113, 131, 139, 157, 163, 173, 191, 193, 199, 211, 223, 241, 251, 269, 271, 277, 293, 311, 313, 331, 353, 373, 379, 397, 419, 421, 439, 443, 457, 463, 499, 509, 521, 523, 541, 577, 601, 607, 613, 619, 631, 653, 659, 661, 673, 691

Offset

1,1

Comments

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..59.

Example

Let p=13. Then we have 5<13/2<7. Since 13>5+7, then 13 is in the sequence.

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. A166574, A182365, A166307, A166252, A166251, A164368, A104272, A080359, A164333, A164288, A164294, A164554

Sequence in context: A129919 A045454 A356833 * A265808 A265790 A002540

Adjacent sequences: A166572 A166573 A166574 * A166576 A166577 A166578

Keyword

nonn

Author

Vladimir Shevelev, Oct 17 2009

Status

approved