A184248 Primes, q, such that for three consecutive primes, p, q & r, with p

3, 5, 7, 13, 19, 31, 43, 53, 61, 73, 103, 109, 139, 151, 157, 173, 181, 193, 199, 211, 229, 241, 257, 263, 271, 283, 313, 349, 373, 401, 421, 433, 463, 467, 491, 509, 523, 563, 571, 593, 601, 607, 619, 643, 653, 661, 733, 743, 761, 811, 823, 829, 859

Offset: 1

Author

Robert G. Wilson v, Jan 10 2011

Keywords

• easy
• nonn

Comments

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

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

Crossrefs

Cf. A184247.

Programs

Mathematica

fQ[n_] := Block[{p = NextPrime[n, -1], q = n, r = NextPrime[n]}, IntegerQ[(r - q)/(q - p)]]; Select[ Prime@ Range@ 150, fQ]
Transpose[Select[Partition[Prime[Range[200]],3,1],IntegerQ[(#[[3]]- #[[2]])/ (#[[2]]-#[[1]])]&]][[2]] (* Harvey P. Dale, Mar 30 2014 *)