A324265 - OEIS

%I #18 Sep 08 2022 08:46:24

%S 5,1715,588245,201768035,69206436005,23737807549715,8142067989552245,

%T 2792729320416420035,957906156902832072005,328561811817671400697715,

%U 112696701453461290439316245,38654968598537222620685472035,13258654229298267358895116908005,4547718400649305704101025099445715

%N a(n) = 5*343^n.

%C x = a(n) and y = A324266(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 7^(6*n+1) = 4*y^3 (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.

%F O.g.f.: 5/(1 - 343*x).

%F E.g.f.: 5*exp(343*x).

%F a(n) = 343*a(n-1) for n > 0.

%F a(n) = (1/25)*(A193577(n))^3.

%e For a(0) = 5 and A324266(0) = 2, 5^2 + 7 = 32 = 4*2^3.

%p a:=n->5*343^n: seq(a(n), n=0..20);

%t 5*343^Range[0,20]

%o (GAP) List([0..20], n->5*343^n);

%o (Magma) [5*343^n: n in [0..20]];

%o (PARI) a(n) = 5*343^n;

%Y Cf. A324266 (2*49^n), A000290 (n^2), A000578 (n^3), A193577 (5*7^n).

%K nonn,easy

%O 0,1

%A _Stefano Spezia_, Feb 20 2019