The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A002733 Numbers k such that (k^2 + 1)/10 is prime. (Formerly M4342 N1047) 4
 7, 13, 17, 23, 27, 33, 37, 53, 63, 67, 77, 87, 97, 103, 113, 127, 137, 147, 153, 163, 167, 197, 223, 227, 247, 263, 267, 277, 283, 287, 297, 303, 323, 347, 363, 367, 373, 383, 397 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Contribution from Wolfdieter Lang, Feb 27 2012: (Start) The corresponding primes (n^2 + 1)/10 are given in A207337(n). a(n) is the smallest positive representative of the class of nontrivial solutions of the congruence x^2 == 1 (Modd A207337(n)), if n >= 2. The trivial solution is the class with representative x=1, which also includes -1. For Modd n see a comment on A203571. For n=1: a(1) = 7 == 3 (Modd 5), and 3 is the smallest positive solution > 1. The unique class of nontrivial solutions of the congruence x^2 == 1 (Modd p), with p an odd prime, exists for any p of the form 4*k+1, given in A002144. Here a subset of these primes is covered, the ones for k = k(n) = (a(n)^2 - 9)/40. These k-values are [1, 4, 7, 13, 18, 27, 34, 70, 99, 112, ...]. (End) REFERENCES L. Euler, De numeris primis valde magnis (E283), reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 3, p. 25. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 L. Euler, De numeris primis valde magnis (E283), The Euler Archive FORMULA a(n) = sqrt(10*A207337(n)-1) = sqrt(8*A207339(n)+1), n >= 1. - Wolfdieter Lang, Feb 27 2012 MAPLE a := [ ]: for n from 1 to 400 do if (n^2+1 mod 10) = 0 and isprime((n^2+1)/10) then a := [ op(a), n ]; fi; od; MATHEMATICA Select[Range[573], PrimeQ[(#^2 + 1)/10] &] (* T. D. Noe, Feb 28 2012 *) PROG (PARI) forstep(n=7, 1e3, [6, 4], if(isprime(n^2\10+1), print1(n", "))) \\ Charles R Greathouse IV, Mar 11 2012 (Haskell) a002733 = a000196 . (subtract 1) . (* 10) . a207337 -- Reinhard Zumkeller, Apr 06 2012 CROSSREFS Cf. A000196, A010051, A002522, A002731, A002732. Sequence in context: A230039 A226138 A180263 * A108334 A288713 A136083 Adjacent sequences: A002730 A002731 A002732 * A002734 A002735 A002736 KEYWORD nonn AUTHOR N. J. A. Sloane STATUS approved

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

Last modified September 9 06:26 EDT 2024. Contains 375759 sequences. (Running on oeis4.)