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A323605 Smallest prime divisor of A000058(n) = A007018(n) + 1 (Sylvester's sequence). 2
2, 3, 7, 43, 13, 3263443, 547, 29881, 5295435634831, 181, 2287, 73 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) is also the smallest prime divisor of A007018(n+1) that is not a divisor of A007018(n).

The prime numbers a(n) are all distinct, which proves the infinitude of the prime numbers (Saidak's proof).

a(12) <= 2589377038614498251653. - Daniel Suteu, Jan 20 2019

LINKS

Table of n, a(n) for n=0..11.

F. Saidak A new proof of Euclid's theorem, Amer. Math. Monthly, 113:10 (2006) 937--938.

Wikipedia,Sylvester's_sequence: Divisibility_and_factorizations

MAPLE

with(numtheory):

u:=1: P:=NULL: to 9 do P:=P, sort([op(divisors(u+1))])[2]: u:=u*(u+1) od:

P;

PROG

(PARI) f(n)=if(n<1, n>=0, f(n-1)+f(n-1)^2); \\ A007018

a(n)=divisors(f(n)+1)[2]; \\ Michel Marcus, Jan 20 2019

CROSSREFS

Cf. A007018, A000058, A007996 (primes that divide at least one term of A000058).

Sequence in context: A000945 A261564 A126263 * A216826 A030087 A106864

Adjacent sequences:  A323602 A323603 A323604 * A323606 A323607 A323608

KEYWORD

nonn,more

AUTHOR

Robert FERREOL, Jan 19 2019

EXTENSIONS

a(10)-a(11) from Daniel Suteu, Jan 20 2019

STATUS

approved

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Last modified April 21 17:36 EDT 2021. Contains 343156 sequences. (Running on oeis4.)