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A007535 Smallest pseudoprime ( > n ) to base n: smallest composite number m > n such that n^(m-1)-1 is divisible by m.
(Formerly M5440)
29

%I M5440

%S 4,341,91,15,124,35,25,9,28,33,15,65,21,15,341,51,45,25,45,21,55,69,

%T 33,25,28,27,65,45,35,49,49,33,85,35,51,91,45,39,95,91,105,205,77,45,

%U 76,133,65,49,66,51,65,85,65,55,63,57,65,133,87,341,91,63,341,65,112,91

%N Smallest pseudoprime ( > n ) to base n: smallest composite number m > n such that n^(m-1)-1 is divisible by m.

%C a(k-1) = k for odd composite numbers k = {9, 15, 21, 25, 27, 33, 35, 39, 45, 49, 51, ...} = A071904(n). - _Alexander Adamchuk_, Dec 13 2006

%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 42 (but beware errors in his table for n = 28, 58, 65, 77, 100).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A007535/b007535.txt">Table of n, a(n) for n = 1..10000</a>

%H G. P. Michon, <a href="http://www.numericana.com/answer/pseudo.htm">Pseudoprimes</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FermatsLittleTheorem.html">Fermat's Little Theorem.</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Pseudoprime">Pseudoprime</a>

%H <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>

%t f[n_] := Block[{k = n + 1}, While[PrimeQ[k] || PowerMod[n, k - 1, k] != 1, k++ ]; k]; Table[ f[n], {n, 67}] (* _Robert G. Wilson v_, Sep 18 2004 *)

%o (Haskell)

%o import Math.NumberTheory.Moduli (powerMod)

%o a007535 n = head [m | m <- dropWhile (<= n) a002808_list,

%o powerMod n (m - 1) m == 1]

%o -- _Reinhard Zumkeller_, Jul 11 2014

%o (PARI) a(n)=forcomposite(m=n+1,, if(Mod(n, m)^(m-1)==1, return(m))) \\ _Charles R Greathouse IV_, May 18 2015

%Y Records in A098653 & A098654.

%Y Cf. A071904, A002808.

%K nonn,nice,easy

%O 1,1

%A _N. J. A. Sloane_, _Mira Bernstein_, _Robert G. Wilson v_

%E Corrected and extended by _Patrick De Geest_, October 2000

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Last modified April 13 09:12 EDT 2021. Contains 342935 sequences. (Running on oeis4.)