A111005 Terms in A062234 that are powers > 1.
9, 9, 27, 25, 81, 125, 225, 225, 361, 441, 1089, 1089, 1225, 1225, 2025, 2025, 2601, 3249, 3249, 3375, 3721, 5041, 6859, 7569, 7921, 12321, 13689, 13689, 15129, 18225, 21609, 21609, 30625, 31329, 38809, 42025, 47961, 53361, 59049, 65025, 65025
Offset: 1
Keywords
Examples
a(20) = 2*prime(478) - prime(479) = 2*3391 - 3407 = 3375 = 15^3.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A062234.
Programs
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Maple
with(numtheory); egcd := proc(n) local L; L:=map(proc(z) z[2] end, ifactors(n)[2]); igcd(op(L)) end: PW:=[]: cnt:=0: for z to 1 do for j from 1 to 50000 do x:=2*ithprime(j)-ithprime(j+1); if egcd(x)>1 then cnt:=cnt+1; PW:=[op(PW),[cnt,j,x]] fi od od; PW; map(proc(z) z[3] end, PW);
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Mathematica
fn[n_]:=2*Prime[n]-Prime[n+1];Select[fn[Range[3,7000]],ResourceFunction["PerfectPowerQ"][#]&] (* James C. McMahon, Apr 27 2024 *)
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PARI
lista(pmax) = {my(prev = 2, k); forprime(p = 3, pmax, k = 2*prev - p; if(ispower(k), print1(k, ", ")); prev = p);} \\ Amiram Eldar, Aug 02 2024
Extensions
Title modified by James C. McMahon, Apr 27 2024