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A034694
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Smallest prime == 1 (mod n).
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50
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Thangadurai and Vatwani prove that a(n) <= 2^(phi(n)+1)-1. - T. D. Noe, Oct 12 2011
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REFERENCES
| S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 127-130.
Graham, D. (1981): On Linnik's Constant. Acta Arithm.,39:163-179.
Niven I. and Powell, B. (1976): Primes in Certain Arithmetic Progressions. Amer. Math. Monthly,83:467-489.
Ribenboim, P. (1989):The Book of Prime Number Records. Chapter 4,IV.B.: The Smallest Prime In Arithmetic Progressions, pp. 217-223.
R. Thangadurai and A. Vatwani, The least prime congruent to one modulo n, Amer. Math. Monthly, Vol. 118, 2011, p. 737-742.
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..10000
S. R. Finch, More about Linnik's Constant
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EXAMPLE
| If n = 7, the smallest prime in the sequence 8,15,22,29,... is 29, so a(7) = 29.
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MATHEMATICA
| f[n_] := Block[{k = 1}, If[n == 1, 2, While[Mod[Prime@k, n] != 1, k++ ]; Prime@k]]; Array[f, 64] (from Robert G. Wilson v (rgwv(at)rgwv.com), Jul 08 2006)
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PROG
| (PARI) a(n)=if(n<0, 0, s=1; while((prime(s)-1)%n>0, s++); prime(s))
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CROSSREFS
| Cf. A034693, A034694, A034780, A034782, A034783, A034784, A034785, A034846, A034847, A034848, A034849.
Cf. A085420. Records: A120856, A120857.
Sequence in context: A085102 A087572 A085107 * A050921 A087386 A110359
Adjacent sequences: A034691 A034692 A034693 * A034695 A034696 A034697
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KEYWORD
| nonn,nice,easy
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AUTHOR
| Labos Elemer (LABOS(AT)ana.sote.hu), David W. Wilson (davidwwilson(AT)comcast.net), Spring 1998
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