The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A102457 Least k >= 2 with n^(kn) == n (mod kn), also n^(kn-1) == 1 (mod k). 5
 80519, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 17, 2, 19, 2, 3, 2, 23, 2, 5, 2, 3, 2, 29, 2, 31, 2, 3, 2, 5, 2, 37, 2, 3, 2, 41, 2, 43, 2, 3, 2, 47, 2, 7, 2, 3, 2, 53, 2, 5, 2, 3, 2, 59, 2, 61, 2, 3, 2, 5, 2, 67, 2, 3, 2, 71, 2, 73, 2, 3, 2, 7, 2, 79, 2, 3, 2, 83, 2, 5, 2, 3, 2, 89, 2, 7, 2, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Motivated by even base-2 pseudoprime 161038, I inquired into base-n pseudoprimes kn that are multiples of n, i.e., n^(kn) == n (mod kn). This is equivalent to n^(kn-1) == 1 (mod k) [W. Edwin Clark] and is satisfied by any k dividing n-1 [Michael Reid]. For n >= 3, this guarantees the existence of a(n) with 2 <= a(n) = k <= lpf(n-1) (lpf = least prime factor). For most n, a(n) = lpf(n-1), exceptional n and a(n) are noted in A102458 and A102459. LINKS Antti Karttunen, Table of n, a(n) for n = 2..12620 Antti Karttunen, Data supplement: n, a(n) computed for n =  2..100000 MATHEMATICA Array[Block[{k = 2}, While[PowerMod[#, k # - 1, k] != 1, k++]; k] &, 93, 2] (* Michael De Vlieger, Nov 13 2018 *) PROG (PARI) A102457(n) = { for(k=2, oo, if(1==(Mod(n, k)^((k*n)-1)), return(k)); ); } \\ Antti Karttunen, Nov 10 2018 CROSSREFS Cf. A102458, A102459. Cf. A092067. - R. J. Mathar, Aug 30 2008 Sequence in context: A251377 A204051 A218248 * A102459 A347906 A329188 Adjacent sequences: A102454 A102455 A102456 * A102458 A102459 A102460 KEYWORD nonn AUTHOR David W. Wilson, Jan 09 2005 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 June 15 22:50 EDT 2024. Contains 373412 sequences. (Running on oeis4.)