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A265261 Smallest n-Knödel number, i.e., smallest composite c > n such that each b < c coprime to c satisfies b^(c-n) == 1 (mod c). 1
561, 4, 9, 6, 25, 8, 15, 12, 21, 12, 15, 16, 33, 24, 21, 20, 65, 24, 51, 24, 45, 24, 33, 32, 69, 30, 39, 40, 65, 36, 87, 40, 45, 44, 51, 40, 85, 56, 57, 48, 65, 72, 91, 48, 63, 66, 69, 60, 141, 56, 63, 60, 65, 72, 75, 60, 63, 70, 87, 72, 133, 122, 93, 80, 165 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Felix Fröhlich, Table of n, a(n) for n = 1..4000

Wikipedia, Knödel number.

MATHEMATICA

Table[SelectFirst[Range[n + 1, 10^3], Function[c, CompositeQ@ c && AllTrue[Range[1, c - 1] /. x_ /; ! CoprimeQ[x, c] -> Nothing, Mod[#^(c - n), c] == 1 &]]], {n, 65}] (* Michael De Vlieger, Apr 06 2016, Version 10 *)

PROG

(PARI) a(n) = forcomposite(c=n+1, , my(i=0, j=0); for(b=1, c-1, if(gcd(b, c)==1, i++; if(Mod(b, c)^(c-n)==1, j++))); if(i==j, return(c)))

CROSSREFS

Cf. A050990, A033553, A050992, A050993, A208154, A208155, A208156, A208157, A208158.

Sequence in context: A167822 A104590 A259211 * A234936 A274443 A247906

Adjacent sequences:  A265258 A265259 A265260 * A265262 A265263 A265264

KEYWORD

nonn

AUTHOR

Felix Fröhlich, Apr 06 2016

STATUS

approved

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Last modified September 25 05:14 EDT 2021. Contains 347652 sequences. (Running on oeis4.)