A179780 Primes, q, such that for three consecutive primes, p, q & r, with p

23, 37, 47, 67, 79, 83, 89, 113, 127, 131, 163, 167, 233, 251, 277, 293, 307, 317, 331, 337, 353, 359, 367, 379, 383, 389, 409, 439, 443, 449, 479, 503, 547, 557, 577, 587, 613, 631, 647, 677, 683, 691, 701, 709, 719, 727, 739, 751, 757, 773, 787, 797, 839, 853, 863

Offset: 1

Author

Robert G. Wilson v, Jan 10 2011

Keywords

• easy
• nonn

Comments

The distance between the cited prime above to its immediate predecessor and the distance from that prime to its immediate successor is a ratio a/b with neither a nor b equal to 1.

Complement(A000040, A184247 & A184248)

Links

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

Crossrefs

Cf. A184247 & A184248.

Programs

Mathematica

fQ[n_] := Block[{p = NextPrime[n, -1], q = n, r = NextPrime[n]}, !IntegerQ[(q - p)/(r - q)] && !IntegerQ[(r - q)/(q - p)]]; Select[ Prime@ Range@ 150, fQ]
Select[Partition[Prime[Range[200]],3,1],NoneTrue[{(#[[2]]-#[[1]])/ (#[[3]]- #[[2]]),(#[[3]]-#[[2]])/(#[[2]]-#[[1]])},IntegerQ]&][[All,2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 20 2016 *)