A084291 Difference between consecutive primes arising after difference (d=2) between twin primes. In A001223, terms succeeding those that equal 2.

2, 4, 4, 4, 6, 4, 6, 6, 4, 4, 10, 6, 10, 4, 12, 4, 10, 6, 10, 4, 4, 10, 6, 4, 18, 6, 6, 12, 4, 12, 10, 4, 10, 4, 4, 10, 6, 10, 6, 4, 10, 6, 4, 6, 4, 6, 4, 6, 4, 4, 4, 6, 24, 10, 10, 12, 4, 10, 16, 22, 4, 10, 4, 10, 16, 6, 10, 4, 4, 22, 6, 6, 6, 16, 4, 4, 6, 10, 6, 16, 28, 10, 16, 12, 4, 12, 6

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

Do[s1=Prime[n]-Prime[n-1]; s=Prime[n+1]-Prime[n]; s2=Prime[n+2]-Prime[n+1]; If[Equal[s, 2], Print[s2]], {n, 1, 10000}]
#[[3]]-#[[2]]&/@Select[Partition[Prime[Range[1000]], 3, 1], #[[2]]- #[[1]] == 2&] (* Harvey P. Dale, Jul 08 2018 *)
Join[{2}, SequenceCases[Differences[Prime[Range[3, 500]]], {2, _}][[;; , 2]]] (* Harvey P. Dale, Mar 20 2023 *)

Prog

(PARI) list(lim) = {my(prv = 3, dprv = 1, d); forprime(p = 5, lim, d = p - prv; if(dprv == 2, print1(d, ", ")); prv = p; dprv = d); } \\ Amiram Eldar, Feb 08 2025

Crossrefs

Cf. A001223, A084290.

Sequence in context: A035633 A160803 A278481 * A258573 A073806 A060849

Adjacent sequences: A084288 A084289 A084290 * A084292 A084293 A084294

Keyword

nonn,changed

Author

Labos Elemer, May 26 2003

Status

approved