A123996 Smallest prime q such that the gap between q and the previous prime is a perfect power that has not occurred earlier as a gap.
3, 11, 97, 1847, 5623, 9587, 89753, 396833, 3851587, 11981587, 70396589, 202551883, 1872852203, 10958688203, 47203303559, 767644375301, 8817792099037, 78610833115937, 497687231721941, 2069461000670881
Offset: 1
Keywords
Examples
a(2)=97 since 97-prevprime(97)=97-89=8 is the first occurrence of 8 as a difference between successive primes.
Links
- Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101].
Programs
-
Maple
with(numtheory); egcd := proc(n::posint) local L; if n>1 then L:=ifactors(n)[2]; L:=map(z->z[2],L); return igcd(op(L)) else return 1 fi end: P:={}; Q:=[]; p:=2; for w to 1 do for k from 0 do # keep track if k mod 10^6 = 0 then print(k,p) fi; lastprime:=p; q:=nextprime(p); d:=q-p; x:=egcd(d); if x>1 and not d in P then P:=P union {d}; Q:=[op(Q), [q,d]]; print(q,d); print(P); print(Q); fi ; p:=q; od od; # let it run with AutoSave enabled. -
Mathematica
NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ@k, k++ ]; k]; perfectPowerQ[x_] := GCD @@ Last /@ FactorInteger@x > 1; dd = {1}; pp = {2}; qq = {3}; p = 3; Do[q = NextPrim@p; d = q - p; If[perfectPowerQ@d && !MemberQ[dd, d], Print@q; AppendTo[qq, q]; AppendTo[dd, d]]; p = q, {n, 10^7}]; qq (* Robert G. Wilson v, Nov 03 2006 *)
Formula
Next prime after A123995.
Extensions
Edited and extended by Robert G. Wilson v, Nov 03 2006, corrected Nov 04 2006
Definition corrected by M. F. Hasler, Oct 19 2018
Comments