A084313 a(n)=x is the smallest number such that gcd(prime(x)-1, x) = n.

1, 2, 21, 16, 5, 6, 315, 24, 63, 20, 121, 12, 65, 14, 105, 320, 697, 306, 2185, 60, 399, 286, 299, 216, 575, 156, 513, 644, 1189, 210, 837, 384, 231, 374, 1505, 684, 3515, 1026, 1131, 1480, 2747, 966, 1591, 1012, 1935, 782, 1645, 1776, 30429, 7600, 3009

Offset: 1

Author

Labos Elemer, Jun 13 2003

Keywords

• nonn

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 4000 terms from Ivan Neretin)

Crossrefs

Cf. A084309-A084316.

Programs

Mathematica

f[x_] := GCD[Prime[x]-1, x] t=Table[0, {256}]; Do[s=f[n]; If[s<257&&t[[s]]==0, t[[s]]=n], {n, 1, 100000}]; t
Table[Module[{x=1},While[GCD[Prime[x]-1,x]!=n,x++];x],{n,60}] (* Harvey P. Dale, Aug 23 2025 *)

Formula

a(n) = Min{x; A084309(x)=n}.