A144717 - OEIS

%I #29 Jan 13 2023 08:41:23

%S 1,2,3,5,7,8,9,11,12,14,17,20,24,30,34,44,72,85,86,92,115,122,125,132,

%T 142,150,161,162,181,186,198,224,248,252,282,283,290,307,319,321,344,

%U 350,376,445,476,567,623,676,682,704,741,749,786,803,806,893,1014,1046

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

%H Jon E. Schoenfield, <a href="/A144717/b144717.txt">Table of n, a(n) for n = 1..505</a> (lists all terms < 10^5)

%e a(1)=1 because a(0) is not defined and 2*1 + 1 = 3 is prime;

%e a(2)=2 because 2*1*2 + 1 = 5 is prime;

%e a(3)=3 because 2*1*2*3 + 1 = 13 is prime;

%e 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.

%t k = 2; a = {}; Do[If[PrimeQ[k n + 1], k = k n; AppendTo[a, n]], {n, 1, 3000}]; a (* _Artur Jasinski_ *)

%t 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 *)

%o (Python)

%o from sympy import isprime

%o from itertools import count, islice

%o def agen(): # generator of terms

%o     an, p = 1, 2

%o     while True:

%o         yield an

%o         an = next(k for k in count(an+1) if isprime(p*k+1))

%o         p *= an

%o print(list(islice(agen(), 58))) # _Michael S. Branicky_, Jan 13 2023

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

%K nonn,nice

%O 1,2

%A _Artur Jasinski_, Sep 19 2008

%E Edited by _N. J. A. Sloane_, Sep 21 2017 following suggestions from Richard C. Schroeppel