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 A034694 Smallest prime == 1 (mod n). 55
 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; text; internal format)
 OFFSET 1,1 COMMENTS Thangadurai and Vatwani prove that a(n) <= 2^(phi(n)+1)-1. - T. D. Noe, Oct 12 2011 Conjecture: a(n) < n^2 for n > 1. - Thomas Ordowski, Dec 19 2016 REFERENCES 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. LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 Steven R. Finch, Linnik's Constant S. Graham, On Linnik's Constant, Acta Arithm. 39, 1981, pp. 163-179. I. Niven and B. Powell, Primes in Certain Arithmetic Progressions, Amer. Math. Monthly 83(6) (1976), 467-469. R. Thangadurai and A. Vatwani, The least prime congruent to one modulo n, Amer. Math. Monthly 118(8) (2011), 737-742. FORMULA a(n) = min{m: m = k*n + 1 with k > 0 and A010051(m) = 1}. - Reinhard Zumkeller, Dec 17 2013 EXAMPLE If n = 7, the smallest prime in the sequence 8, 15, 22, 29, ... is 29, so a(7) = 29. MATHEMATICA f[n_] := Block[{k = 1}, If[n == 1, 2, While[Mod[Prime@k, n] != 1, k++ ]; Prime@k]]; Array[f, 64] (* Robert G. Wilson v, Jul 08 2006 *) With[{prs=Prime[Range[200]]}, Join[{2}, Flatten[Table[Select[prs, Mod[#, n] == 1&, 1], {n, 2, 70}]]]] (* Harvey P. Dale, Mar 16 2012 *) PROG (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) -- Reinhard Zumkeller, Dec 17 2013 CROSSREFS Cf. A034693, A034780, A034782, A034783, A034784, A034785, A034846, A034847, A034848, A034849, A038700, A085420. Records: A120856, A120857. Sequence in context: A085107 A241082 A219789 * A050921 A087386 A110359 Adjacent sequences:  A034691 A034692 A034693 * A034695 A034696 A034697 KEYWORD nonn,nice,easy,changed AUTHOR Labos Elemer, David W. Wilson, Spring 1998 STATUS approved

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Last modified October 22 04:25 EDT 2019. Contains 328315 sequences. (Running on oeis4.)