A324270 - OEIS

%I #11 Sep 08 2022 08:46:24

%S 13,10706059,8816899947037,7261096233082692091,

%T 5979824975081619492698413,4924642999453642161875329137259,

%U 4055655269699050826917294183685688637,3340006507773765415151949203915063077180891,2750638979431530091290481703239822791770782516813,2265269477037980585971637173331233381403285546243728459

%N a(n) = 13*7^(7*n).

%C x = a(n) and y = A324266(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 7^(14*n+3) = 4*y^7 (see Theorem 2.1 in Chakraborty, Hoque and Sharma).

%H K. Chakraborty, A. Hoque, R. Sharma, <a href="https://arxiv.org/abs/1812.11874">Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations</a>, arXiv:1812.11874 [math.NT], 2018.

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (823543).

%F O.g.f.: 13/(1 - 823543*x).

%F E.g.f.: 13*exp(823543*x).

%F a(n) = 823543*a(n-1) for n > 0.

%F a(n) = 13*823543^n.

%F a(n) = A008595(A001015((A000420(n)))).

%e For a(0) = 13 and A324266(0) = 2, 13^2 + 7^3 = 512 = 4*2^7.

%p a:=n->13*823543^n: seq(a(n), n=0..20);

%t 13 823543^Range[0, 20]

%o (GAP) List([0..20], n->13*823543^n);

%o (Magma) [13*823543^n: n in [0..20]];

%o (PARI) a(n) = 13*823543^n;

%Y Cf. A324266 (2*49^n), A001015 (seventh powers), A000420 (powers of 7), A008595 (multiples of 13).

%K nonn,easy

%O 0,1

%A _Stefano Spezia_, Mar 22 2019