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

A133072 a(n) = n^5 + n^3 - n^2.

Original entry on oeis.org

0, 1, 36, 261, 1072, 3225, 7956, 17101, 33216, 59697, 100900, 162261, 250416, 373321, 540372, 762525, 1052416, 1424481, 1895076, 2482597, 3207600, 4092921, 5163796, 6447981, 7975872, 9780625, 11898276, 14367861, 17231536, 20534697, 24326100, 28657981, 33586176, 39170241, 45473572
Offset: 0

Views

Author

Omar E. Pol, Nov 01 2007

Keywords

Comments

Exponents are the prime numbers in decreasing order.

Examples

			a(7)=17101 because 7^5=16807, 7^3=343, 7^2=49 and we can write 16807+343-49=17101.

Links

Crossrefs

Cf. A000290, A000578, A000584, A011379, A045991, A100019.
Cf. A133070, A133071, 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 + 30*x + 60*x^2 + 26*x^3 + 3*x^4)/(1-x)^6. - R. J. Mathar, Nov 14 2007

Extensions

More terms from Vincenzo Librandi, Dec 15 2010

A134633 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, 10, 192, 1314, 5344, 16050, 39600, 85162, 165504, 297594, 503200, 809490, 1249632, 1863394, 2697744, 3807450, 5255680, 7114602, 9465984, 12401794, 16024800, 20449170, 25801072, 32219274, 39855744, 48876250, 59460960, 71805042, 86119264, 102630594, 121582800, 143237050, 167872512, 195786954, 227297344
Offset: 0

Views

Author

Omar E. Pol, Nov 04 2007

Keywords

Examples

			a(4)=5344 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=5344.

Links

Crossrefs

Cf. A000290, A000578, A000584, A045991, A100019, A133073.

Programs

  • Magma
    [5*n^5+3*n^3+2*n^2: n in [0..50]]; // Vincenzo Librandi, Dec 14 2010
  • Maple
    A134633:=n->5*n^5 + 3*n^3 + 2*n^2; seq(A134633(n), n=0..50); # Wesley Ivan Hurt, May 21 2014
  • Mathematica
    Table[5n^5+3n^3+2n^2,{n,0,40}] (* or *) LinearRecurrence[ {6,-15,20,-15,6,-1},{0,10,192,1314,5344,16050},40] (* Harvey P. Dale, Apr 25 2012 *)
CoefficientList[Series[2 x (5 + 66 x + 156 x^2 + 70 x^3 + 3x^4)/(1 - x)^6, {x, 0, 50}], x] (* Vincenzo Librandi, May 21 2014 *)

Formula

a(n) = 5*n^5 + 3*n^3 + 2*n^2.
G.f.: 2x*(5+66x+156x^2+70x^3+3x^4)/(1-x)^6. - R. J. Mathar, Nov 14 2007
a(0)=0, a(1)=10, a(2)=192, a(3)=1314, a(4)=5344, a(5)=16050, 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). - Harvey P. Dale, Apr 25 2012

Extensions

More terms from Vincenzo Librandi, Dec 14 2010

A133064 a(n) = 5*p^5 + 3*p^3 + 2*p^2, where p = prime(n).

Original entry on oeis.org

192, 1314, 16050, 85162, 809490, 1863394, 7114602, 12401794, 32219274, 102630594, 143237050, 346874482, 579491130, 735284434, 1147040922, 2091429714, 3575244594, 4223669890, 6751536802, 9022230570, 10366535674, 15386773594, 19696932354, 27922427994, 42939458122, 52553613810
Offset: 1

Views

Author

Omar E. Pol, Nov 05 2007

Keywords

Examples

			a(4)=85162 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 = 85162.

Crossrefs

Cf. A000290, A000578, A000584, A045991, A133073, A000040 (prime numbers).

Programs

  • Magma
    [5*p^5+3*p^3+2*p^2: p in PrimesUpTo(200)] // Vincenzo Librandi, Dec 15 2010
  • Mathematica
    5#^5+3#^3+2#^2&/@Prime[Range[30]] (* Harvey P. Dale, Dec 17 2011 *)
  • PARI
    a(n) = my(p=prime(n)); 5*p^5 + 3*p^3 + 2*p^2; \\ Michel Marcus, Mar 11 2022

Formula

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

Extensions

More terms from Vincenzo Librandi, Dec 15 2010
Showing 1-5 of 5 results.

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