A242742 Let k be the n-th composite number: then a(n) is the smallest base b such that b^(k-1) == 1 (mod k).

5, 7, 9, 8, 11, 13, 15, 4, 17, 19, 21, 8, 23, 25, 7, 27, 26, 9, 31, 33, 10, 35, 6, 37, 39, 14, 41, 43, 45, 8, 47, 49, 18, 51, 16, 9, 55, 21, 57, 20, 59, 61, 63, 8, 65, 8, 25, 69, 22, 11, 73, 75, 26, 45, 34, 79, 81, 80, 83, 85, 4, 87, 28, 89, 91, 3, 93, 32, 95

Offset: 1

Author

Felix Fröhlich, Aug 16 2014

Keywords

• nonn

Links

• Felix Fröhlich, Table of n, a(n) for n = 1..8769 (all terms up to k=10^4)

Crossrefs

Cf. A002808, A001567, A105222, A181780, A211455, A211456, A211457, A211458.

Programs

Mathematica

sbb[n_]:=Module[{b=2},While[PowerMod[b,n-1,n]!=1,b++];b]; sbb/@Select[ Range[ 100],CompositeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 29 2018 *)

PARI

forcomposite(k=2, 1e2, for(b=2, 1e9, if(Mod(b, k)^(k-1)==1, print1(b, ", "); next({2}))); print1(">1e9, "))

Formula

a(n) = A105222(A002808(n)). - Michel Marcus, Aug 21 2014