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 1-4 of 4 results.

A001594 a(n) = 6^n + n^6.

Original entry on oeis.org

1, 7, 100, 945, 5392, 23401, 93312, 397585, 1941760, 10609137, 61466176, 364568617, 2179768320, 13065520825, 78371693632, 470196375201, 2821126684672, 16926683582305, 101559990680640, 609359787056377
Offset: 0

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Author

Keywords

Crossrefs

Cf. sequences of the form k^n+n^k: A001580 (k=2), A001585 (k=3), A001589 (k=4), A001593 (k=5), this sequence (k=6), A001596 (k=7), A198401 (k=8), A185277 (k=9), A177068 (k=10), A177069 (k=11).

Programs

  • Magma
    [6^n+n^6: n in [0..30]]; // Vincenzo Librandi, Oct 27 2011
    
  • Maple
    seq(seq(k^n+n^k, k=6..6), n=0..19); # Zerinvary Lajos, Jun 29 2007
  • Mathematica
    Table[6^n + n^6, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 6 x + 72 x^2 - 75 x^3 - 1475 x^4 - 1776 x^5 - 334 x^6 - 7 x^7)/((1-x)^7 (1-6 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 28 2014 *)
    LinearRecurrence[{13,-63,161,-245,231,-133,43,-6},{1,7,100,945,5392,23401,93312,397585},20] (* Harvey P. Dale, Jan 07 2023 *)
  • PARI
    a(n)=6^n+n^6 \\ Charles R Greathouse IV, Feb 14 2011
    
  • Sage
    [6^n+n^6 for n in (0..30)] # Bruno Berselli, Aug 28 2014

Formula

G.f.: (1 - 6*x + 72*x^2 - 75*x^3 - 1475*x^4 - 1776*x^5 - 334*x^6 - 7*x^7)/((1-x)^7*(1-6*x)). - Vincenzo Librandi, Aug 28 2014

A177069 11^n + n^11.

Original entry on oeis.org

1, 12, 2169, 178478, 4208945, 48989176, 364568617, 1996813914, 8804293473, 33739007300, 125937424601, 570623341222, 3881436747409, 36314872537968, 383799398752905, 4185897925275026, 45967322049616577, 505481300395601404
Offset: 0

Views

Author

Vincenzo Librandi, May 31 2010

Keywords

Crossrefs

Cf. sequences of the form k^n+n^k: A001580 (k=2), A001585 (k=3), A001589 (k=4), A001593 (k=5), A001594 (k=6), A001596 (k=7), A198401 (k=8), A185277 (k=9), A177068 (k=10), this sequence (k=11).

Programs

  • Magma
    [11^n+n^11: n in [0..20]]
    
  • Mathematica
    Table[11^n + n^11, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 11 x + 2091 x^2 + 130021 x^3 + 524976 x^4 -14501046 x^5 - 91394082 x^6 - 163229406 x^7 - 104915271 x^8 - 24085951 x^9 - 1676905 x^10 - 22407 x^11 - 10 x^12)/((1 - x)^12 (1 - 11 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 28 2014 *)
  • PARI
    a(n)= 11^n+n^11 \\ Charles R Greathouse IV, Jan 11 2012
    
  • Sage
    [11^n+n^11 for n in (0..30)] # Bruno Berselli, Aug 28 2014

Formula

G.f.: (1 - 11*x + 2091*x^2 + 130021*x^3 + 524976*x^4 - 14501046*x^5 - 91394082*x^6 - 163229406*x^7 - 104915271*x^8 - 24085951*x^9 - 1676905*x^10 - 22407*x^11 - 10*x^12) / ((1-x)^12*(1-11*x)). - Vincenzo Librandi, Aug 28 2014

A198401 a(n) = 8^n + n^8.

Original entry on oeis.org

1, 9, 320, 7073, 69632, 423393, 1941760, 7861953, 33554432, 177264449, 1173741824, 8804293473, 69149458432, 550571544609, 4399522300160, 35186934979457, 281479271677952, 2251806789442689, 18014409529442560, 144115205059418913
Offset: 0

Views

Author

Vincenzo Librandi, Oct 27 2011

Keywords

Crossrefs

Programs

  • Magma
    [8^n+n^8: n in [0..20]]
    
  • Mathematica
    f[n_] := 8^n + n^8; f[Range[0, 30]]
    LinearRecurrence[{17,-108,372,-798,1134,-1092,708,-297,73,-8},{1,9,320,7073,69632,423393,1941760,7861953,33554432,177264449},30] (* Harvey P. Dale, Aug 26 2023 *)
  • PARI
    a(n)=8^n+n^8 \\ Charles R Greathouse IV, Oct 16 2015

Formula

G.f.: -(9*x^9 +1966*x^8 +34133*x^7 +120575*x^6 +109459*x^5 +18599*x^4 -2233*x^3 -275*x^2 +8*x -1) / ((x -1)^9*(8*x -1)). - Colin Barker, Sep 13 2013

A276203 Numbers k such that k^9 + 9^k is prime.

Original entry on oeis.org

2, 76, 122, 422, 2300, 5090, 7166, 58046, 91382, 234178, 314738
Offset: 1

Views

Author

Felix Fröhlich, Aug 27 2016

Keywords

Comments

Numbers k such that A185277(k) is prime.

Examples

			2 is a term of the sequence, because A185277(2) = 593 is prime.
		

Crossrefs

Programs

  • PARI
    is(n) = ispseudoprime(n^9+9^n)
Showing 1-4 of 4 results.