A267291 Primes which are at 2/3 of the distance between their neighbors.

11, 17, 41, 71, 97, 101, 107, 197, 227, 281, 311, 397, 457, 461, 487, 499, 617, 769, 827, 857, 881, 937, 1091, 1301, 1427, 1447, 1451, 1487, 1543, 1567, 1579, 1667, 1697, 1787, 1871, 1877, 1901, 1997, 2087, 2141, 2381, 2411, 2539, 2609, 2617, 2687, 2707, 2711, 2749, 2801, 3019, 3061, 3109, 3167, 3181, 3203, 3217, 3257

Offset

1,1

Comments

Or: primes p such that p = (prevprime(p) + 2 nextprime(p))/3, Or, p=prime(k) such that prime(k)-prime(k-1) = 2(prime(k+1)-prime(k)). See A194581 for primes which are at 1/3 of the distance between their neighbors.

Links

Table of n, a(n) for n=1..58.

Example

11 is in the sequence because 11 = (7 + 2*13) / 3.

Mathematica

Select[Prime@ Range@ 480, # == (NextPrime[#, -1] + 2 NextPrime@ #)/3 &] (* Michael De Vlieger, Jan 12 2016 *)

Prog

(PARI) a(n, show=0, o=2, g=0)={forprime(p=o+1, , g==2*(g=-o+o=p)||next; show&&print1(p-g", "); n--||return(p-g))} \\ 2nd & 3rd optional args allow printing the whole list and using another starting value.

Crossrefs

Cf. A194581.

Sequence in context: A147253 A201476 A057473 * A073649 A178070 A243222

Adjacent sequences: A267288 A267289 A267290 * A267292 A267293 A267294

Keyword

nonn

Author

M. F. Hasler, Jan 12 2016

Status

approved