

A290585


a(n) is the largest number <= n such that 1 + a(1)*a(2)*...*a(n) is prime.


2



1, 2, 3, 3, 4, 6, 6, 4, 7, 7, 3, 10, 13, 12, 10, 9, 13, 14, 15, 16, 13, 21, 22, 11, 25, 26, 27, 17, 29, 23, 7, 11, 30, 24, 34, 1, 1, 1, 1, 1, 1, 1, 1, 1, 45, 39, 23, 48, 32, 25, 44, 49, 53, 31, 1, 1, 1, 1, 59, 46, 53, 55, 62, 40, 62, 59, 46, 41, 9, 62, 59, 64, 1, 1, 1, 1, 1, 1, 1, 80, 57, 78, 80, 1, 85
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OFFSET

1,2


COMMENTS

a(n) = n for n = 1, 2, 3, 6, 13, 25, 26, 27, 29, 45, 48, 53, 59, 80, 85, ...
If a(n) = 1, then the next entry > 1 is a(m) = m for the least m > n such that 1 + m * Product_{j=1..n1} a_j is prime. By Dirichlet's theorem such m exists.  Robert Israel, Aug 07 2017


LINKS



MAPLE

A[1]:= 1: P:= 1:
for n from 2 to 200 do
for k from n to 0 by 1 do
if isprime(1+k*P) then
A[n]:= k;
P:= P*k;
break
fi
od;
od:


MATHEMATICA

p = 1; Table[t = SelectFirst[Range[n, 1, 1], PrimeQ[1 + p #] &]; p *= t; t, {n, 85}] (* Giovanni Resta, Aug 08 2017 *)


PROG

(Python)
from sympy import isprime
A=[0, 1]
p=1
for n in range(2, 201):
for k in range(n, 1, 1):
if isprime(1 + k*p):
A.append(k)
p*=k
break
(PARI) first(n) = { my(i = 1, res = vector(n)); res[1]=1; for(x=2, n, forstep(k=x, 0, 1, if(ispseudoprime(1+k*i), res[x]=k; i*=k; break()))); res; } \\ Iain Fox, Nov 15 2017


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



