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.
%I A382809 #15 Jul 18 2025 10:32:53
%S A382809 1,1729,12025,38665,89425,172081,294409,464185,689185,977185,1335961,
%T A382809 1773289,2296945,2914705,3634345,4463641,5410369,6482305,7687225,
%U A382809 9032905,10527121,12177649,13992265,15978745,18144865,20498401,23047129,25798825,28761265,31942225,35349481
%N A382809 a(n) = (6*n + 1)*(12*n + 1)*(18*n + 1).
%C A382809 a(n) is a Carmichael number if all the three factors (6*n + 1), (12*n + 1), and (18*n + 1) are prime (see Chernick and Ribenboim).
%D A382809 Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 101.
%D A382809 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 146.
%H A382809 Jack Chernick, <a href="https://doi.org/10.1090/S0002-9904-1939-06953-X">On Fermat's simple theorem</a>, Bulletin of the American Mathematical Society, Vol. 45, No. 4 (1939), pp. 269-274.
%H A382809 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A382809 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 3.
%F A382809 G.f.: (1 + 1725*x + 5115*x^2 + 935*x^3)/(1 - x)^4.
%F A382809 E.g.f.: exp(x)*(1 + 1728*x + 4284*x^2 + 1296*x^3).
%F A382809 a(n) = A016921(n) * A017533(n) * A161705(n).
%F A382809 a(n) == 1 (mod 72).
%t A382809 LinearRecurrence[{4,-6,4,-1},{1,1729,12025,38665},31]
%Y A382809 Cf. A002997, A033502, A046025.
%Y A382809 Cf. A002476, A002997, A016921, A017533, A068228, A161705.
%K A382809 nonn,easy
%O A382809 0,2
%A A382809 _Stefano Spezia_, Apr 05 2025