

A144717


a(n) = smallest positive integer > a(n1) such that 2*a(1)*a(2)*...*a(n) + 1 is prime.


12



1, 2, 3, 5, 7, 8, 9, 11, 12, 14, 17, 20, 24, 30, 34, 44, 72, 85, 86, 92, 115, 122, 125, 132, 142, 150, 161, 162, 181, 186, 198, 224, 248, 252, 282, 283, 290, 307, 319, 321, 344, 350, 376, 445, 476, 567, 623, 676, 682, 704, 741, 749, 786, 803, 806, 893, 1014, 1046
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OFFSET

1,2


LINKS



EXAMPLE

a(1)=1 because a(0) is not defined and 2*1 + 1 = 3 is prime;
a(2)=2 because 2*1*2 + 1 = 5 is prime;
a(3)=3 because 2*1*2*3 + 1 = 13 is prime;
a(4) is not 4 because 2*1*2*3*4 + 1 = 49 is not prime, but a(4)=5 works because 2*1*2*3*5 + 1 = 61 is prime.


MATHEMATICA

k = 2; a = {}; Do[If[PrimeQ[k n + 1], k = k n; AppendTo[a, n]], {n, 1, 3000}]; a (* Artur Jasinski *)
nxt[{p_, a_}]:=Module[{k=a+1}, While[!PrimeQ[p*k+1], k++]; {p*k, k}]; NestList[ nxt, {2, 1}, 60][[All, 2]] (* Harvey P. Dale, Aug 18 2021 *)


PROG

(Python)
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
an, p = 1, 2
while True:
yield an
an = next(k for k in count(an+1) if isprime(p*k+1))
p *= an


CROSSREFS

Cf. A046966, A046972, A144718, A144722, A144723, A144724, A144725, A144726, A144727, A144728, A144729, A144730, A144731.


KEYWORD

nonn,nice


AUTHOR



EXTENSIONS

Edited by N. J. A. Sloane, Sep 21 2017 following suggestions from Richard C. Schroeppel


STATUS

approved



