Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Nov 11 2023 10:39:49
%S 15,85,4369,16843009,281479271743489,79228162532711081671548469249,
%T 6277101735386680764176071790128604879584176795969512275969
%N Products of two consecutive Fermat numbers: a(n) = A000215(n) * A000215(n+1).
%C a(7) has 116 digits and is too large to include in the data section.
%C Szymiczek (1966) proved that a(n) is a super-Poulet number (A050217) for all n >= 2. All the composite Fermat numbers (A281576) are also super-Poulet numbers.
%D Michal Krížek, Florian Luca and Lawrence Somer, 17 Lectures on Fermat Numbers, Springer-Verlag, N.Y., 2001, p. 142.
%H Amiram Eldar, <a href="/A367228/b367228.txt">Table of n, a(n) for n = 0..10</a>
%H Andrzej Rotkiewicz, <a href="https://eudml.org/doc/35153">On pseudoprimes having special forms and a solution of K. Szymiczek's problem</a>, Acta Mathematica Universitatis Ostraviensis, Vol. 13, No. 1 (2005), pp. 57-71.
%H Kazimierz Szymiczek, <a href="https://www.e-periodica.ch/digbib/view?pid=edm-001%3A1966%3A21%3A%3A4&referrer=search#65">Note on Fermat numbers</a>, Elemente der Mathematik, Vol. 21, No. 3 (1966), p. 59.
%F a(n) = (2^(2^n) + 1) * (2^(2^(n+1)) + 1).
%t f[n_] := 2^(2^n) + 1; a[n_] := f[n] * f[n + 1]; Array[a, 7, 0]
%o (PARI) f(n) = 2^(2^n) + 1;
%o a(n) = f(n) * f(n+1);
%Y Cf. A000215, A050217, A281576.
%K nonn,easy
%O 0,1
%A _Amiram Eldar_, Nov 11 2023