login
A324267
a(n) = 11*7^(5*n).
0
11, 184877, 3107227739, 52223176609373, 877714929273732011, 14751754816303613908877, 247932743197614838966495739, 4167005614922312598509893885373, 70034863369999307843155786531464011, 1177075948659578366919919304234315632877, 19783115469121533612823083746266142841763739
OFFSET
0,1
COMMENTS
x = a(n) and y = A324266(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 7^(10*n+1) = 4*y^5 (see Theorem 2.1 in Chakraborty, Hoque and Sharma).
FORMULA
a(n) = 11*16807^n.
O.g.f.: 11/(1 - 16807*x).
E.g.f.: 11*exp(16807*x).
a(n) = 16807*a(n-1) for n > 0.
a(n) = 11*((7/2)*A109808(n))^5.
EXAMPLE
For a(0) = 11 and A324266(0) = 2, 11^2 + 7 = 128 = 4*2^5.
MAPLE
a:=n->11*16807^n: seq(a(n), n=0..20);
MATHEMATICA
11*16807^Range[0, 20]
PROG
(GAP) List([0..20], n->11*16807*n);
(Magma) [11*16807^n: n in [0..20]];
(PARI) a(n) = 11*16807^n;
CROSSREFS
Cf. A324266: 2*49^n; A000290: n^2; A000584: n^5; A109808: 2*7^(n-1).
Sequence in context: A022009 A201249 A144837 * A085017 A239203 A098880
KEYWORD
nonn,easy
AUTHOR
Stefano Spezia, Feb 26 2019
STATUS
approved