A117646 Triples of three consecutive primes (p,q,r) with equal gaps: q-p = r-q.

3, 5, 7, 47, 53, 59, 151, 157, 163, 167, 173, 179, 199, 211, 223, 251, 257, 263, 257, 263, 269, 367, 373, 379, 557, 563, 569, 587, 593, 599, 601, 607, 613, 647, 653, 659, 727, 733, 739, 941, 947, 953, 971, 977, 983, 1097, 1103, 1109, 1117, 1123, 1129, 1181, 1187, 1193

Offset

1,1

Comments

Not monotone: a(18) = 263 > 257 = a(19). - Charles R Greathouse IV, Dec 17 2016

Links

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

Maple

f:= n-> (l-> `if`(l[2]-l[1]=l[3]-l[2], l, [])[])(map(ithprime, [$n..n+2])):
map(f, [$1..194])[];  # Alois P. Heinz, Mar 31 2026

Mathematica

a = Delete[Union[Flatten[Table[If[(Prime[n] + 2*m - Prime[n + 1] == 0) && (Prime[n + 1] + 2*m - Prime[ n + 2] == 0), {Prime[n], Prime[n + 1], Prime[ n + 2]}, {}], {m, 1, 17}, {n, 1, 200}], 1]], 1] Flatten[a]
Select[Partition[Prime[Range[200]], 3, 1], Length[Union[Differences[#]]] == 1&]// Flatten (* Harvey P. Dale, Dec 23 2018 *)

Prog

(PARI) p=2; q=3; forprime(r=5, 1e4, if(q-p==r-q, print1(p", "q", "r", ")); p=q; q=r) \\ Charles R Greathouse IV, Dec 17 2016

Crossrefs

Columns 1-3 give A122535, A006562, A181424.

Cf. A064113.

Sequence in context: A102742 A363965 A089044 * A064857 A065913 A137999

Adjacent sequences: A117643 A117644 A117645 * A117647 A117648 A117649

Keyword

nonn,tabf,less

Author

Roger L. Bagula, Apr 10 2006

Extensions

Edited by Sean A. Irvine, Mar 31 2026

Status

approved