A046966 a(n) is the smallest number > a(n-1) such that a(1)*a(2)*...*a(n) + 1 is prime.

1, 2, 3, 5, 6, 9, 12, 16, 22, 25, 29, 31, 35, 47, 57, 61, 66, 79, 81, 108, 114, 148, 163, 172, 185, 198, 203, 205, 236, 265, 275, 282, 294, 312, 344, 359, 377, 397, 398, 411, 427, 431, 493, 512, 589, 647, 648, 660, 708, 719, 765, 887, 911, 916, 935, 1062, 1093

Offset: 1

Author

G. L. Honaker, Jr.

Keywords

• nonn
• nice

Examples

			1*2*3*5 + 1 = 31 is prime.
		

References

• H. Dubner, Recursive Prime Generating Sequences, Table 4 pp. 173 Journal of Recreational Mathematics 29(3) 1998 Baywood NY.

Links

• Charles R Greathouse IV and T. D. Noe, Table of n, a(n) for n = 1..500 (first 200 terms from Noe)

Crossrefs

Cf. A046972.

Programs

Mathematica

a[1] = 1; p[1] = 1;
a[n_] := a[n] = For[an = a[n-1] + 1, True, an++, pn = p[n-1]*an; If[ PrimeQ[pn+1], p[n] = pn; Return[an] ] ];
Table[a[n], {n, 1, 60}]
(* Jean-François Alcover, Sep 17 2012 *)
Module[{cc={1},k},Do[k=Last[cc]+1;While[!PrimeQ[Times@@Join[cc,{k}]+1], k++];AppendTo[cc,k],{60}];cc] (* Harvey P. Dale, Jan 21 2013 *)
nxt[{t_,a_}]:=Module[{k=a+1},While[CompositeQ[t*k+1],k++];{t*k,k}]; NestList[nxt,{1,1},60][[All,2]] (* Harvey P. Dale, May 22 2021 *)

PARI

first(n)=my(v=vector(n),N=1,t=1); v[1]=1; for(k=2,n, while(!ispseudoprime(1 + N*t++),); N*=v[k]=t); v \\ Charles R Greathouse IV, Apr 07 2020

Extensions

More terms from Jason Earls, Jan 25 2002

Definition corrected by T. D. Noe, Feb 14 2007