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 1-5 of 5 results.

A133070 a(n) = n^5 - n^3 - n^2.

Original entry on oeis.org

0, -1, 20, 207, 944, 2975, 7524, 16415, 32192, 58239, 98900, 159599, 246960, 368927, 534884, 755775, 1044224, 1414655, 1883412, 2468879, 3191600, 4074399, 5142500, 6423647, 7948224, 9749375, 11863124, 14328495, 17187632, 20485919, 24272100, 28598399, 33520640, 39098367, 45394964
Offset: 0

Views

Author

Omar E. Pol, Nov 01 2007

Keywords

Comments

Exponents are prime numbers in decreasing order.

Examples

			a(7)=16415 because 7^5=16807, 7^3=343, 7^2=49 and we can write 16807-343-49=16415.

Links

Crossrefs

Cf. A000290, A000578, A000584, A011379, A045991, A100019.
Cf. A133071, A133072, A133073.

Programs

  • Magma
    [n^5-n^3-n^2: n in [0..50]]; // Vincenzo Librandi, Dec 15 2010
  • Mathematica
    Table[n^5-n^3-n^2,{n,0,40}] (* or *) LinearRecurrence[ {6,-15,20,-15,6,-1},{0,-1,20,207,944,2975},41] (* Harvey P. Dale, Jul 23 2011 *)
  • PARI
    for(n=0,50, print1(n^5 - n^3 - n^2, ", ")) \\ G. C. Greubel, Oct 20 2017

Formula

a(n) = n^5 - n^3 - n^2.
G.f.: x*(-1 +26*x + 72*x^2 + 22*x^3 + x^4)/(1-x)^6. - R. J. Mathar, Nov 14 2007
a(n) = 6*a(n-1) -15*a(n-2) +20*a(n-3) -15*a(n-4) +6*a(n-5) -a(n-6), with a(0)=0, a(1)=-1, a(2)=20, a(3)=207, a(4)=944, a(5)=2975. - Harvey P. Dale, Jul 23 2011

Extensions

More terms from Vincenzo Librandi, Dec 15 2010

A133071 a(n) = n^5 - n^3 + n^2.

Original entry on oeis.org

0, 1, 28, 225, 976, 3025, 7596, 16513, 32320, 58401, 99100, 159841, 247248, 369265, 535276, 756225, 1044736, 1415233, 1884060, 2469601, 3192400, 4075281, 5143468, 6424705, 7949376, 9750625, 11864476, 14329953, 17189200, 20487601, 24273900, 28600321, 33522688, 39100545, 45397276
Offset: 0

Views

Author

Omar E. Pol, Nov 01 2007

Keywords

Comments

Exponents are prime numbers in decreasing order.

Examples

			a(7)=16513 because 7^5=16807, 7^3=343, 7^2=49 and we can write 16807-343+49=16513.

Links

Crossrefs

Cf. A000290, A000578, A000584, A011379, A045991, A100019.
Cf. A133070, A133072, A133073.

Programs

  • Magma
    [n^5-n^3+n^2: n in [0..50]]; // Vincenzo Librandi, Dec 15 2010
  • Mathematica
    Table[n^5 - n^3 + n^2, {n,0,50}] (* G. C. Greubel, Oct 20 2017 *)
  • PARI
    for(n=0,50, print1(n^5 - n^3 + n^2, ", ")) \\ G. C. Greubel, Oct 20 2017

Formula

a(n) = n^5 - n^3 + n^2.
G.f.: x*(1 + 22*x + 72*x^2 + 26*x^3 - x^4)/(1-x)^6. - R. J. Mathar, Nov 14 2007

Extensions

More terms from Vincenzo Librandi, Dec 15 2010

A133073 a(n) = n^5 + n^3 + n^2.

Original entry on oeis.org

0, 3, 44, 279, 1104, 3275, 8028, 17199, 33344, 59859, 101100, 162503, 250704, 373659, 540764, 762975, 1052928, 1425059, 1895724, 2483319, 3208400, 4093803, 5164764, 6449039, 7977024, 9781875, 11899628, 14369319, 17233104, 20536379, 24327900, 28659903, 33588224, 39172419, 45475884
Offset: 0

Views

Author

Omar E. Pol, Nov 01 2007

Keywords

Comments

Exponents are prime numbers in decreasing order.

Examples

			a(7) = 17199 because 7^5 = 16807, 7^3 = 343, 7^2 = 49 and we can write 16807 + 343 + 49 = 17199.

Links

Crossrefs

Cf. A000290, A000578, A000584, A011379, A045991, A100019.
Cf. A133070, A133071, A133072.

Programs

  • Magma
    [n^5+n^3+n^2: n in [0..50]]; // Vincenzo Librandi, Dec 15 2010
  • Mathematica
    Total[#^{5,3,2}]&/@Range[0,40]  (* Harvey P. Dale, Jan 18 2011 *)
LinearRecurrence[{6,-15,20,-15,6,-1},{0,3,44,279,1104,3275},35] (* James C. McMahon, Mar 10 2025 *)
  • PARI
    for(n=0,50, print1(n^5 + n^3 + n^2, ", ")) \\ G. C. Greubel, Oct 20 2017

Formula

G.f.: x*(3 + 26*x + 60*x^2 + 30*x^3 + x^4)/(1-x)^6. - R. J. Mathar, Nov 14 2007
a(n) = n^2*(n^3 + n + 1). - Wesley Ivan Hurt, Mar 02 2023

Extensions

More terms from Vincenzo Librandi, Dec 15 2010

A133063 a(n) = 5*p^5 + 3*p^3 - 2*p^2, where p = prime(n).

Original entry on oeis.org

176, 1278, 15950, 84966, 809006, 1862718, 7113446, 12400350, 32217158, 102627230, 143233206, 346869006, 579484406, 735277038, 1147032086, 2091418478, 3575230670, 4223655006, 6751518846, 9022210406, 10366514358, 15386748630, 19696904798, 27922396310, 42939420486, 52553573006
Offset: 1

Views

Author

Omar E. Pol, Nov 05 2007

Keywords

Examples

			a(4)=84966 because the 4th prime is 7, 5*7^5=84035, 3*7^3=1029, 2*7^2=98 and we can write 84035+1029-98=84966.

Links

Crossrefs

Cf. A000290, A000578, A000584, A045991, A133072. Prime numbers: A000040.

Programs

  • Magma
    [5*p^5+3*p^3-2*p^2: p in PrimesUpTo(200)]; // Vincenzo Librandi, Dec 15 2010
  • Maple
    a:= n-> (p-> (5*p^3+3*p-2)*p^2)(ithprime(n)):
seq(a(n), n=1..26);  # Alois P. Heinz, Sep 23 2024
  • Mathematica
    Table[(Prime[n])^2*(5*Prime[n]^3 + 3*Prime[n] - 2), {n, 1, 50}] (* G. C. Greubel, Oct 09 2017 *)
  • PARI
    for(n=1,25, print1(5*prime(n)^5 + 3*prime(n)^3 - 2*prime(n)^2, ", ")) \\ G. C. Greubel, Oct 09 2017

Formula

a(n) = 5*(p(n))^5 + 3*(p(n))^3 - 2*(p(n))^2, where p(n)=A000040(n).

Extensions

More terms from Vincenzo Librandi, Dec 15 2010

A134632 5*n^5 + 3*n^3 - 2*n^2. Coefficients and exponents are the prime numbers in decreasing order.

Original entry on oeis.org

0, 6, 176, 1278, 5280, 15950, 39456, 84966, 165248, 297270, 502800, 809006, 1249056, 1862718, 2696960, 3806550, 5254656, 7113446, 9464688, 12400350, 16023200, 20447406, 25799136, 32217158, 39853440, 48873750, 59458256, 71802126, 86116128, 102627230, 121579200, 143233206, 167868416, 195782598, 227292720
Offset: 0

Views

Author

Omar E. Pol, Nov 04 2007

Keywords

Examples

			a(4)=5280 because 4^5=1024, 5*1024=5120, 4^3=64, 3*64=192, 4^2=16, 2*16=32 and we can write 5120+192-32=5280.

Links

Crossrefs

Cf. A000290, A000578, A000584, A045991, A100019, A133072.

Programs

Formula

a(n) = 5*n^5 + 3*n^3 - 2*n^2.
G.f.: 2x*(3+70x+156x^2+66x^3+5x^4)/(1-x)^6. - R. J. Mathar, Nov 14 2007

Extensions

More terms from Vincenzo Librandi, Dec 14 2010
Showing 1-5 of 5 results.

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