A152587 Generalized Fermat numbers: a(n) = 14^(2^n) + 1.
15, 197, 38417, 1475789057, 2177953337809371137, 4743480741674980702700443299789930497, 22500609546641425009067997918450033531906583365663182830821882796510806017
Offset: 0
Examples
a(0) = 14^1+1 = 15 = 13*(1)+2 = 13(empty product)+2. a(1) = 14^2+1 = 197 = 13*(15)+2. a(2) = 14^4+1 = 38417 = 13*(15*197)+2. a(3) = 14^8+1 = 1475789057 = 13*(15*197*38417)+2. a(4) = 14^16+1 = 2177953337809371137 = 13*(15*197*38417*1475789057)+2. a(5) = 14^32+1 = 4743480741674980702700443299789930497 = 13*(15*197*38417*1475789057*2177953337809371137)+2.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 0..9
- Anders Björn and Hans Riesel, Factors of Generalized Fermat Numbers, Mathematics of Computation, Vol. 67, No. 221, Jan., 1998, pp. 441-446.
- OEIS Wiki, Generalized Fermat numbers
Crossrefs
Cf. A000215.
Programs
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Magma
[14^(2^n) + 1: n in [0..8]]; // Vincenzo Librandi, Jun 20 2011
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Mathematica
Table[14^2^n+1,{n,0,7}] (* Harvey P. Dale, Jun 10 2023 *) -
PARI
g(a,n) = if(a%2,b=2,b=1);for(x=0,n,y=a^(2^x)+b;print1(y","))
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PARI
a(n)=14^(2^n)+1 \\ Charles R Greathouse IV, Jul 29 2011
Formula
a(0) = 15, a(n) = (a(n-1)-1)^2 + 1, n >= 1.
a(n) = 13*a(n-1)*a(n-2)*...*a(1)*a(0) + 2, n >= 0, where for n = 0, we get 13*(empty product, i.e., 1)+ 2 = 15 = a(0). This implies that the terms, all odd, are pairwise coprime. - Daniel Forgues, Jun 20 2011
Comments