cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A070592 Largest prime factor of the n-th Fermat number F(n) = 2^(2^n) + 1.

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%I A070592 #28 Apr 03 2025 15:01:11
%S A070592 3,5,17,257,65537,6700417,67280421310721,5704689200685129054721,
%T A070592 93461639715357977769163558199606896584051237541638188580280321
%N A070592 Largest prime factor of the n-th Fermat number F(n) = 2^(2^n) + 1.
%D A070592 Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 72.
%H A070592 Eric M. Schmidt, <a href="/A070592/b070592.txt">Table of n, a(n) for n = 0..11</a>
%H A070592 C. L. Stewart, <a href="https://doi.org/10.1112/plms/s3-35.3.425">On Divisors of Fermat, Fibonacci, Lucas, and Lehmer Numbers</a>, Proceedings of the London Mathematical Society, Vol. s3-35, No. 3 (1977), pp. 425-447. See p. 430.
%H A070592 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FermatNumber.html">Fermat Number</a>.
%F A070592 From _Amiram Eldar_, Oct 25 2024: (Start)
%F A070592 a(n) = A006530(A000215(n)).
%F A070592 a(n) > c * n * 2^n for n >= 1, where c is a positive absolute constant (Stewart, 1977). (End)
%o A070592 (PARI) a(n) = vecmax(factor(2^(2^n) + 1)[,1]); \\ _Michel Marcus_, Jul 05 2017
%Y A070592 Cf. A000215, A006530, A050922, A093179.
%K A070592 nonn,hard
%O A070592 0,1
%A A070592 _Benoit Cloitre_, May 12 2002
%E A070592 Offset changed by _Arkadiusz Wesolowski_, Jul 09 2011