Search: id:A014566
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%I A014566
%S A014566 2,2,5,28,257,3126,46657,823544,16777217,387420490,10000000001,
%T A014566 285311670612,8916100448257,302875106592254,11112006825558017,
%U A014566 437893890380859376,18446744073709551617,827240261886336764178
%N A014566 Sierpinski numbers of the first kind: n^n + 1.
%C A014566 Sierpinski primes of the form n^n + 1 are {2,5,257,...} = A121270. The 
               prime p divides a((p-1)/2) for p = {5,7,13,23,29,31,37,47,53,61,71,
               ...} = A003628 Primes congruent to {5, 7} mod 8. p^2 divides a((p-1)/
               2) for prime p = {29,37,3373,...}. - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Sep 11 2006
%C A014566 n divides a(n-1) for even n, or 2n divides a(2n-1). a(2n-1)/(2n) = A124899(n) 
               = {1, 7, 521, 102943, 38742049, 23775972551, 21633936185161, 27368368148803711, 
               45957792327018709121, ...}. 2^n divides a(2^n-1). A014566[2^n - 1] 
               / 2^n = A081216[2^n - 1] = A122000[n] = {1, 7, 102943, 27368368148803711, 
               533411691585101123706582594658103586126397951, ...}. p+1 divides 
               a(p) for prime p. a(p)/(p+1) = A056852[n] = {7, 521, 102943, 23775972551, 
               21633936185161, ...}. p^2 divides a((p-1)/2) for prime p = {29, 37, 
               3373} = A121999(n). - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Nov 12 2006
%D A014566 G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence 
               Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
%D A014566 M. Le, Primes in the sequences n^n+1 and n^n-1, Smarandache Notions Journal, 
               Vol. 10, No. 1-2-3, 1999, 156-157.
%D A014566 P. Ribenboim, The Book of Prime Number Records, 2nd ed. New York: Springer-Verlag, 
               p. 74, 1989.
%D A014566 F. Smarandache, Only Problems, Not Solutions!, Xiquan Publ. Hse., 1990, 
               Problem 17.
%H A014566 M. F. Hasler, <a href="b014566.txt">Table of n,a(n) for n=0,...,100</
               a>
%H A014566 M. L. Perez et al., eds., <a href="http://www.gallup.unm.edu/~smarandache/
               ">Smarandache Notions Journal</a>
%H A014566 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">
               Only Problems, Not Solutions!</a>.
%H A014566 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SierpinskiNumberoftheFirstKind.html">Link to a section of The World 
               of Mathematics.</a>
%F A014566 For n>0, resultant of x^n+1 and nx-1. - Ralf Stephan, Nov 20 2004
%t A014566 a(0) = 2; for n>0 Table[n^n+1,{n,1,20}] - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Sep 11 2006
%o A014566 (PARI) A014566(n)=n^n+1 /* M. F. Hasler (www.univ-ag.fr/~mhasler), Jan 
               21 2009 */
%Y A014566 Cf. A000312, A048861, A121270, A003628, A122000, A081216, A056852, A121999, 
               A124899.
%Y A014566 Sequence in context: A019099 A154647 A103890 this_sequence A076658 A020549 
               A114715
%Y A014566 Adjacent sequences: A014563 A014564 A014565 this_sequence A014567 A014568 
               A014569
%K A014566 nonn,easy
%O A014566 0,1
%A A014566 Eric Weisstein (eric(AT)weisstein.com)
%E A014566 More terms from Erich Friedman (erich.friedman(AT)stetson.edu).

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