A084316 a(n) is the smallest number x such that gcd(prime(x)+1,x+1) = n.

1, 3, 20, 11, 24, 5, 6, 39, 98, 29, 120, 23, 64, 13, 104, 15, 1716, 323, 284, 499, 62, 1099, 1264, 215, 1274, 51, 512, 447, 1768, 209, 1332, 31, 32, 373, 34, 1475, 258, 835, 2300, 519, 5780, 419, 5374, 1275, 6974, 1655, 6626, 479, 10240, 10549, 3008, 883, 13938

Offset

1,2

Comments

a(n) == n+1 (mod 2). - Robert Israel, May 04 2017

Links

Ivan Neretin, Table of n, a(n) for n = 1..4000 (first 2880 terms from Robert Israel)

Formula

a(n) = Min{x; A066752(x)=n}.

Example

In A066752, n=5 arises first at the 24th position, so a(5)=24.

Maple

f:= proc(n) local x;
  for x from n-1 by ilcm(n, 2) do
    if igcd(x+1, ithprime(x)+1) = n then return x fi
  od
end proc:
f(1):= 1:
map(f, [$1..100]); # Robert Israel, May 04 2017

Mathematica

f[x_]:=GCD[Prime[x]+1, x+1]; t=Table[0, {256}]; Do[s=f[n]; If[s<257&&t[[s]] == 0, t[[s]] = n], {n, 1, 100000}]; t (* edited by Harvey P. Dale, Jan 28 2023 *)
Module[{nn=20000, t}, t=Table[{x, GCD[Prime[x]+1, x+1]}, {x, nn}]; Table[SelectFirst[t, #[[2]]==n&], {n, 60}]][[All, 1]] (* Harvey P. Dale, Jan 28 2023 *)

Crossrefs

Cf. A000040, A066752, A084309-A084315.

Sequence in context: A223282 A223480 A063871 * A126810 A115280 A212995

Adjacent sequences: A084313 A084314 A084315 * A084317 A084318 A084319

Keyword

nonn

Author

Labos Elemer, Jun 13 2003

Status

approved