cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A324265 a(n) = 5*343^n.

Original entry on oeis.org

5, 1715, 588245, 201768035, 69206436005, 23737807549715, 8142067989552245, 2792729320416420035, 957906156902832072005, 328561811817671400697715, 112696701453461290439316245, 38654968598537222620685472035, 13258654229298267358895116908005, 4547718400649305704101025099445715
Offset: 0

Views

Author

Stefano Spezia, Feb 20 2019

Keywords

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).

Examples

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

Links

Crossrefs

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

Programs

  • GAP
    List([0..20], n->5*343^n);
  • Magma
    [5*343^n: n in [0..20]];
  • Maple
    a:=n->5*343^n: seq(a(n), n=0..20);
  • Mathematica
    5*343^Range[0,20]
  • PARI
    a(n) = 5*343^n;

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.

A324267 a(n) = 11*7^(5*n).

Original entry on oeis.org

11, 184877, 3107227739, 52223176609373, 877714929273732011, 14751754816303613908877, 247932743197614838966495739, 4167005614922312598509893885373, 70034863369999307843155786531464011, 1177075948659578366919919304234315632877, 19783115469121533612823083746266142841763739
Offset: 0

Views

Author

Stefano Spezia, Feb 26 2019

Keywords

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).

Examples

			For a(0) = 11 and A324266(0) = 2, 11^2 + 7 = 128 = 4*2^5.

Links

Crossrefs

Cf. A324266: 2*49^n; A000290: n^2; A000584: n^5; A109808: 2*7^(n-1).

Programs

  • GAP
    List([0..20], n->11*16807*n);
  • Magma
    [11*16807^n: n in [0..20]];
  • Maple
    a:=n->11*16807^n: seq(a(n), n=0..20);
  • Mathematica
    11*16807^Range[0,20]
  • PARI
    a(n) = 11*16807^n;

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.

A324270 a(n) = 13*7^(7*n).

Original entry on oeis.org

13, 10706059, 8816899947037, 7261096233082692091, 5979824975081619492698413, 4924642999453642161875329137259, 4055655269699050826917294183685688637, 3340006507773765415151949203915063077180891, 2750638979431530091290481703239822791770782516813, 2265269477037980585971637173331233381403285546243728459
Offset: 0

Views

Author

Stefano Spezia, Mar 22 2019

Keywords

Comments

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).

Examples

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

Links

Crossrefs

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

Programs

  • GAP
    List([0..20], n->13*823543^n);
  • Magma
    [13*823543^n: n in [0..20]];
  • Maple
    a:=n->13*823543^n: seq(a(n), n=0..20);
  • Mathematica
    13 823543^Range[0, 20]
  • PARI
    a(n) = 13*823543^n;

Formula

O.g.f.: 13/(1 - 823543*x).
E.g.f.: 13*exp(823543*x).
a(n) = 823543*a(n-1) for n > 0.
a(n) = 13*823543^n.
a(n) = A008595(A001015((A000420(n)))).
Showing 1-3 of 3 results.

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