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A034694
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Smallest prime == 1 (mod n).
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61
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2, 3, 7, 5, 11, 7, 29, 17, 19, 11, 23, 13, 53, 29, 31, 17, 103, 19, 191, 41, 43, 23, 47, 73, 101, 53, 109, 29, 59, 31, 311, 97, 67, 103, 71, 37, 149, 191, 79, 41, 83, 43, 173, 89, 181, 47, 283, 97, 197, 101, 103, 53, 107, 109, 331, 113, 229, 59, 709, 61, 367, 311
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OFFSET
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1,1
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COMMENTS
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Thangadurai and Vatwani prove that a(n) <= 2^(phi(n)+1)-1. - T. D. Noe, Oct 12 2011
Eric Bach and Jonathan Sorenson show that, assuming GRH, a(n) <= (1 + o(1))*(phi(n)*log(n))^2 for n > 1. See the abstract of their paper in the Links section. - Jianing Song, Nov 10 2019
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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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge, 2003, section 2.12, pp. 127-130.
P. Ribenboim, The Book of Prime Number Records. Chapter 4,IV.B.: The Smallest Prime In Arithmetic Progressions, 1989, pp. 217-223.
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LINKS
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FORMULA
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EXAMPLE
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If n = 7, the smallest prime in the sequence 8, 15, 22, 29, ... is 29, so a(7) = 29.
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MATHEMATICA
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a[n_] := Block[{k = 1}, If[n == 1, 2, While[Mod[Prime@k, n] != 1, k++ ]; Prime@k]]; Array[a, 64] (* Robert G. Wilson v, Jul 08 2006 *)
With[{prs=Prime[Range[200]]}, Flatten[Table[Select[prs, Mod[#-1, n]==0&, 1], {n, 70}]]] (* Harvey P. Dale, Sep 22 2021 *)
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PROG
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(PARI) a(n)=if(n<0, 0, s=1; while((prime(s)-1)%n>0, s++); prime(s))
(Haskell)
a034694 n = until ((== 1) . a010051) (+ n) (n + 1)
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CROSSREFS
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Cf. A034693, A034780, A034782, A034783, A034784, A034785, A034846, A034847, A034848, A034849, A038700, A085420.
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KEYWORD
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nonn,nice,easy
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AUTHOR
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STATUS
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approved
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