A057459 a(n+1) = smallest prime p in the range a(n) < p < a(1)*a(2)*...*a(n) such that p-1 divides a(1)*a(2)*...*a(n); or if no such prime p exists, then a(n+1) = smallest prime > a(n).

2, 3, 5, 7, 11, 23, 31, 43, 47, 67, 71, 139, 211, 283, 311, 331, 431, 463, 659, 683, 691, 863, 947, 967, 1291, 1303, 1319, 1367, 1427, 1699, 1867, 1979, 1987, 2011, 2111, 2131, 2311, 2531, 3011, 3083, 4099, 4423, 4643, 4691, 4831, 5171, 5179, 5683, 5839

Offset: 1

Author

Robert G. Wilson v, Sep 26 2000

Keywords

• nonn

Examples

			a(3) = 5. Since the product of a(1)*a(2) is 6, there is no prime p < 6 such that p-1 | 6 so the next prime greater than a(2) is 5.
a(9) = 47 since 46 (2*23) | 2*3*5*7*11*23*31*43.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007459. See A282027 for another version.

Programs

Maple

with(numtheory): a:=[2]; P:=1; j:=1;
for n from 2 to 36 do
sw:=-1; P:=P*a[n-1];
  for i from j+1 to 1000 do
  if (ithprime(i)N. J. A. Sloane, Feb 13 2017

Mathematica

f[s_List] := Block[{b = Times @@ s, p = NextPrime@ Sort[s][[-1]]}, While[ Mod[b, p -1] > 0 && p < b, p = NextPrime@ p]; If[p > b, p = 2; While[ MemberQ[s, p], p = NextPrime@ p]]; Append[s, p]];; Nest[ f, {2}, 50] (* and modified by Robert G. Wilson v, Feb 13 2017 *)