A214523 a(1) = 13, a(n) is smallest prime of the form k*a(n-1) + 1.

13, 53, 107, 643, 7717, 30869, 432167, 6050339, 12100679, 169409507, 9148113379, 439109442193, 5269313306317, 84309012901073, 7587811161096571, 303512446443862841, 69807862682088453431, 2652698781919361230379, 143245734223645506440467

Offset

1,1

Comments

Sequence does not begin with a(1) = 2 or 3 (13 = 6*2+1 = 4*3*1; but 2*2+1 =5 or 2*3 +1 = 7 are smaller) , because this would be A061092 or A059411.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..300

Example

53 = 4*13 + 1 ; 107 = 2*53 + 1.

Mathematica

t = {13}; Do[k = 1; While[p = k*t[[-1]] + 1; ! PrimeQ[p], k++]; AppendTo[t, p], {20}]; t (* T. D. Noe, Jul 24 2012 *)
nxt[n_]:=Module[{k=1}, While[!PrimeQ[k*n+1], k++]; n*k+1]; NestList[nxt, 13, 20] (* Harvey P. Dale, Apr 28 2014 *)

Prog

(PARI)  a=13; for(n=1, 200, b=a*n+1; if(isprime(b), a=b; print1(a, ", "); next(n=1)))

Crossrefs

Cf. A061092, A059411.

Sequence in context: A262287 A307749 A031905 * A087880 A228872 A041322

Adjacent sequences: A214520 A214521 A214522 * A214524 A214525 A214526

Keyword

nonn

Author

Robin Garcia, Jul 23 2012

Status

approved