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A267291 Primes which are at 2/3 of the distance between their neighbors. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 12 17:59 EST 2019. Contains 329960 sequences. (Running on oeis4.)