The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A034694 Smallest prime == 1 (mod n). 58
 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 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 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 Eric Bach and Jonathan Sorenson, Explicit bounds for primes in residue classes, Mathematics of Computation, 65(216) (1996), 1717-1735. 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 a(n) = n * A034693(n) + 1. - Joerg Arndt, Oct 18 2020 EXAMPLE If n = 7, the smallest prime in the sequence 8, 15, 22, 29, ... is 29, so a(7) = 29. MATHEMATICA 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]]}, 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 AUTHOR Labos Elemer, David W. Wilson, Spring 1998 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 15 06:12 EDT 2021. Contains 342975 sequences. (Running on oeis4.)