A184247 Primes, q, such that for three consecutive primes, p, q & r, with p<q<r, (q - p)/(r - q) is an integer.

5, 11, 17, 29, 41, 53, 59, 71, 97, 101, 107, 137, 149, 157, 173, 179, 191, 197, 211, 223, 227, 239, 257, 263, 269, 281, 311, 347, 373, 397, 419, 431, 457, 461, 487, 499, 521, 541, 563, 569, 593, 599, 607, 617, 641, 653, 659, 673, 733, 769, 809, 821, 827, 857

Offset

1,1

Comments

The distance between the cited prime above to its immediate predecessor is divisible by the distance from that prime to its immediate successor.

Intersection(A184247, A184248): 5, 53, 157, 173, 211, ..., = A006562: Balanced primes (of order 1).

Links

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

Mathematica

fQ[n_] := Block[{p = NextPrime[n, -1], q = n, r = NextPrime[n]}, IntegerQ[(q - p)/(r - q)]]; Select[ Prime@ Range[2, 50], fQ]
Select[Partition[Prime[Range[150]], 3, 1], IntegerQ[(#[[2]]-#[[1]])/(#[[3]]- #[[2]])]&][[All, 2]] (* Harvey P. Dale, Jul 26 2018 *)

Crossrefs

Cf. A184248.

Sequence in context: A028388 A277718 A067606 * A046135 A331946 A162336

Adjacent sequences: A184244 A184245 A184246 * A184248 A184249 A184250

Keyword

easy,nonn

Author

Robert G. Wilson v, Jan 10 2011

Status

approved