The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A324265 a(n) = 5*343^n. 1
 5, 1715, 588245, 201768035, 69206436005, 23737807549715, 8142067989552245, 2792729320416420035, 957906156902832072005, 328561811817671400697715, 112696701453461290439316245, 38654968598537222620685472035, 13258654229298267358895116908005, 4547718400649305704101025099445715 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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). 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.: 5/(1 - 343*x). E.g.f.: 5*exp(343*x). a(n) = 343*a(n-1) for n > 0. a(n) = (1/25)*(A193577(n))^3. EXAMPLE For a(0) = 5 and A324266(0) = 2, 5^2 + 7 = 32 = 4*2^3. MAPLE a:=n->5*343^n: seq(a(n), n=0..20); MATHEMATICA 5*343^Range[0, 20] PROG (GAP) List([0..20], n->5*343^n); (Magma) [5*343^n: n in [0..20]]; (PARI) a(n) = 5*343^n; CROSSREFS Cf. A324266 (2*49^n), A000290 (n^2), A000578 (n^3), A193577 (5*7^n). Sequence in context: A122465 A203683 A330057 * A003733 A201300 A024073 Adjacent sequences: A324262 A324263 A324264 * A324266 A324267 A324268 KEYWORD nonn,easy AUTHOR Stefano Spezia, Feb 20 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 14:54 EST 2022. Contains 358510 sequences. (Running on oeis4.)