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 1-6 of 6 results.

A140719 Primes in A153257.

Original entry on oeis.org

11, 89, 167, 431, 1187, 1559, 3119, 5471, 7559, 18899, 34781, 41579, 57719, 67157, 89009, 108191, 122399, 154439, 270269, 283007, 309671, 628487, 650759, 770039, 875327, 960299, 1213379, 1547207, 1800719, 1845491, 1984247, 2608751, 2724119
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 11 2008

Keywords

Examples

			3^3-4^2=27-16=11, 5^3-6^2=125-36=89, 6^3-7^2=216-49=167,...

Links

Crossrefs

Cf. A153257.

Programs

  • Maple
    R:= NULL: count:= 0:
for n from 2 while count < 100 do
  p:= n^3 - (n+1)^2;
  if isprime(p) then
    count:=count+1; R:= R,p;
  fi
od:
R; # Robert Israel, Oct 19 2021
  • Mathematica
    Select[ #^3 - (# + 1)^2 & /@ Range[2, 140], PrimeQ@ # &] (* Robert G. Wilson v, Aug 17 2008 *)

Extensions

More terms from Robert G. Wilson v, Aug 17 2008

A153258 n^3 - (n+2)^2.

Original entry on oeis.org

-4, -8, -8, 2, 28, 76, 152, 262, 412, 608, 856, 1162, 1532, 1972, 2488, 3086, 3772, 4552, 5432, 6418, 7516, 8732, 10072, 11542, 13148, 14896, 16792, 18842, 21052, 23428, 25976, 28702, 31612, 34712, 38008, 41506, 45212, 49132, 53272, 57638
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Dec 22 2008

Keywords

Links

Crossrefs

Cf. A045991, A081437, A069778, A153257

Programs

  • Mathematica
    a[n_] := n^3-(n+2)^2; lst={}; Do[AppendTo[lst, a[n]], {n, 0, 5!}]; lst

Formula

G.f.: 2*x*(x^3+4*x-2)/(x-1)^4. [Colin Barker, Oct 08 2012]

A153259 a(n)=n^3-(3*(n+3))^2.

Original entry on oeis.org

-81, -143, -217, -297, -377, -451, -513, -557, -577, -567, -521, -433, -297, -107, 143, 459, 847, 1313, 1863, 2503, 3239, 4077, 5023, 6083, 7263, 8569, 10007, 11583, 13303, 15173, 17199, 19387, 21743, 24273, 26983, 29879, 32967, 36253, 39743
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Dec 22 2008

Keywords

Links

Crossrefs

Cf. A045991, A081437, A069778, A153257, A153258.

Programs

  • Mathematica
    a[n_]:=n^3-(3*(n+3))^2;lst={};Do[AppendTo[lst,a[n]],{n,0,5!}];lst
Table[n^3-(3(n+3))^2,{n,0,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{-81,-143,-217,-297},40] (* Harvey P. Dale, Jul 10 2013 *)
  • PARI
    a(n)=n^3-(3*n+9)^2 \\ Charles R Greathouse IV, Oct 18 2022

Formula

a(1)=-81, a(2)=-143, a(3)=-217, a(4)=-297, a(n)=4*a(n-1)-6*a(n-2)+ 4*a(n-3)- a(n-4). - Harvey P. Dale, Jul 10 2013

A168297 a(n) = n^3 + (1-n)^2.

Original entry on oeis.org

1, 1, 9, 31, 73, 141, 241, 379, 561, 793, 1081, 1431, 1849, 2341, 2913, 3571, 4321, 5169, 6121, 7183, 8361, 9661, 11089, 12651, 14353, 16201, 18201, 20359, 22681, 25173, 27841, 30691, 33729, 36961, 40393, 44031, 47881, 51949, 56241, 60763, 65521
Offset: 0

Views

Author

Vladimir Joseph Stephan Orlovsky, Nov 22 2009

Keywords

Links

Crossrefs

Cf. A153257.

Programs

  • Magma
    [n^3+(1-n)^2: n in [0..40]]; // Vincenzo Librandi, Jul 18 2016
  • Mathematica
    Table[n^3 + (1 - n)^2, {n, 0, 50}] (* or *) LinearRecurrence[{4,-6,4,-1}, {1, 1, 9, 31}, 50] (* G. C. Greubel, Jul 17 2016 *)
  • PARI
    a(n)=n^3+(n-1)^2 \\ Charles R Greathouse IV, Oct 18 2022

Formula

G.f.: (1 - 3*x + 11*x^2 - 3*x^3)/(1-x)^4. - R. J. Mathar, Nov 24 2009
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - G. C. Greubel, Jul 17 2016

Extensions

Flipped/normalized the sign of n - R. J. Mathar, Nov 24 2009
Further edited by N. J. A. Sloane, Nov 24 2009

A153260 a(n) = n^3 - 3*(n+3)^2.

Original entry on oeis.org

-27, -47, -67, -81, -83, -67, -27, 43, 149, 297, 493, 743, 1053, 1429, 1877, 2403, 3013, 3713, 4509, 5407, 6413, 7533, 8773, 10139, 11637, 13273, 15053, 16983, 19069, 21317, 23733, 26323, 29093, 32049, 35197, 38543, 42093, 45853, 49829, 54027
Offset: 0

Views

Author

Vladimir Joseph Stephan Orlovsky, Dec 22 2008

Keywords

Links

Crossrefs

Cf. A045991, A081437, A069778, A153257, A153258, A153259.

Programs

  • Magma
    [n^3-3*(n+3)^2: n in [0..40] ]; // Vincenzo Librandi, Aug 25 2011
  • Mathematica
    a[n_]:=n^3-3*(n+3)^2; a/@ Range[0, 50]
Table[n^3-3(n+3)^2,{n,0,50}] (* or *) LinearRecurrence[{4,-6,4,-1},{-27,-47,-67,-81},51] (* Harvey P. Dale, Aug 24 2011 *)
  • PARI
    vector(40, n, n--; n^3-3*(n+3)^2) \\ G. C. Greubel, Nov 10 2018

Formula

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=-27, a(1)=-47, a(2)=-67, a(3)=-81. - Harvey P. Dale, Aug 24 2011
G.f.: (x*(x*(13*x - 41) + 61) - 27)/(x-1)^4. - Harvey P. Dale, Aug 24 2011
E.g.f.: (-27 - 20*x + x^3)*exp(x). - G. C. Greubel, Nov 10 2018

Extensions

Offset changed from 1 to 0 by Vincenzo Librandi, Aug 25 2011

A178617 a(n) = n^4 - (n+1)^3.

Original entry on oeis.org

-1, -7, -11, 17, 131, 409, 953, 1889, 3367, 5561, 8669, 12913, 18539, 25817, 35041, 46529, 60623, 77689, 98117, 122321, 150739, 183833, 222089, 266017, 316151, 373049, 437293, 509489, 590267, 680281, 780209, 890753, 1012639, 1146617
Offset: 0

Views

Author

Vladimir Joseph Stephan Orlovsky, May 30 2010

Keywords

Examples

			-7 is an element since 1^4 - 2^3 = 1 - 8 = -7,
-11 is an element since 2^4 - 3^3 = 16 - 27 = -11.

Links

Crossrefs

Cf. A028387, A153257.

Programs

  • GAP
    List([0..40], n -> n^4-(n+1)^3); # G. C. Greubel, Jan 29 2019
  • Magma
    [n^4-(n+1)^3: n in [0..40]]; // G. C. Greubel, Jan 29 2019
  • Mathematica
    Table[n^4-(n+1)^3,{n,0,40}]
LinearRecurrence[{5,-10,10,-5,1},{-1,-7,-11,17,131},40] (* Harvey P. Dale, Jan 30 2013 *)
  • PARI
    vector(40, n, n--; n^4-(n+1)^3) \\ G. C. Greubel, Jan 29 2019
  • Sage
    [n^4-(n+1)^3 for n in (0..40)] # G. C. Greubel, Jan 29 2019

Formula

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5), where a(0)=-1, a(1)=-7, a(2)=-11, a(3)=17, a(4)=131. - Harvey P. Dale, Jan 30 2013
From G. C. Greubel, Jan 29 2019: (Start)
G.f.: (-1 - 2*x + 14*x^2 + 12*x^3 + x^4)/(1-x)^5.
E.g.f.: (-1 - 6*x + x^2 + 5*x^3 + x^4)*exp(x). (End)
Showing 1-6 of 6 results.

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