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A035094
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Smallest prime of form (n!)*k + 1.
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0
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2, 3, 7, 73, 241, 2161, 15121, 161281, 1088641, 10886401, 39916801, 958003201, 18681062401, 1133317785601, 9153720576001, 83691159552001, 1778437140480001, 12804747411456001, 851515702861824001, 41359334139002880001, 766364132575641600001, 20232013099996938240001
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OFFSET
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1,1
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COMMENTS
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This is one possible generalization of "the least prime problem in special arithmetic progressions" when n in nk+1 is replaced by n!.
a(n) is the smallest prime p such that the multiplicative group modulo p has a subgroup of order n!. - Joerg Arndt, Oct 18 2020
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LINKS
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EXAMPLE
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a(5)=241 because in arithmetic progression 120k+1=5!k+1 the second term is prime, 241.
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MATHEMATICA
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sp[n_]:=Module[{nf=n!, k=1}, While[!PrimeQ[nf*k+1], k++]; nf*k+1]; Array[sp, 20] (* Harvey P. Dale, Jan 27 2013 *)
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PROG
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(PARI) a(n) = for(k=1, oo, if(isprime(k*n! + 1), return(k*n! + 1))); \\ Daniel Suteu, Oct 18 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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