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A323605
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Smallest prime divisor of A000058(n) = A007018(n) + 1 (Sylvester's sequence).
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3
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2, 3, 7, 43, 13, 3263443, 547, 29881, 5295435634831, 181, 2287, 73
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OFFSET
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0,1
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COMMENTS
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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
a(12)..a(50) = [?, 52387, 13999, 17881, 128551, 635263, ?, ?, 352867, 387347773, ?, 74587, ?, ?, 27061, 164299, 20929, 1171, ?, 1679143, ?, ?, 120823, 2408563, 38218903, 333457, 30241, 4219, 1085443, 7603, 1861, ?, 23773, 51769, 1285540933, 429547, ?, 8323570543, ?], where ? denote unknown values > 10^10. - Max Alekseyev, Oct 11 2023
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LINKS
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FORMULA
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MAPLE
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with(numtheory):
u:=1: P:=NULL: to 9 do P:=P, sort([op(divisors(u+1))])[2]: u:=u*(u+1) od:
P;
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PROG
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(PARI) f(n)=if(n<1, n>=0, f(n-1)+f(n-1)^2); \\ A007018
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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