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A324268 a(n) = 31*11^(5*n). 1
31, 4992581, 804060162631, 129494693251885181, 20855249842909360285231, 3358758842450395383296737781, 540931470335478626875322916367831, 87117554228999168336897631003955550381, 14030369226134545059825700370818045344410431, 2259604994238194616429988870420617020762644322981 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
x = a(n) and y = A324269(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 11^(10*n+1) = 4*y^5 (see Theorem 2.1 in Chakraborty, Hoque and Sharma).
LINKS
K. Chakraborty, A. Hoque, R. Sharma, Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations, arXiv:1812.11874 [math.NT], 2018.
FORMULA
O.g.f.: 31/(1 - 161051*x).
E.g.f.: 31*exp(161051*x).
a(n) = 161051*a(n-1) for n > 0.
a(n) = 31*161051^n.
a(n) = 31*A001020(n)^5.
EXAMPLE
For a(0) = 31 and A324269(0) = 3, 31^2 + 11 = 972 = 4*3^5.
MAPLE
a:=n->31*161051^n: seq(a(n), n=0..20);
MATHEMATICA
31 161051^Range[0, 20]
PROG
(GAP) List([0..20], n->31*161051^n);
(Magma) [31*161052^n: n in [0..20]];
(PARI) a(n) = 31*161051^n;
CROSSREFS
Cf. A324269: 3*11^(2*n); A000290: n^2; A000584: n^5; A001020: 11^n.
Sequence in context: A051155 A342118 A216791 * A145210 A091308 A023927
KEYWORD
nonn,easy
AUTHOR
Stefano Spezia, Feb 26 2019
STATUS
approved

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Last modified June 14 01:54 EDT 2024. Contains 373391 sequences. (Running on oeis4.)