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.

A154787 a(n) = A061357(n)*n = A154786(n)/2.

Original entry on oeis.org

0, 0, 0, 4, 5, 6, 7, 16, 18, 20, 22, 36, 26, 28, 45, 32, 51, 72, 19, 60, 84, 66, 69, 120, 100, 78, 135, 84, 87, 180, 62, 160, 198, 68, 175, 216, 148, 190, 273, 160, 164, 336, 172, 176, 405, 184, 188, 336, 147, 300, 408, 260, 265, 432, 330, 392, 570
Offset: 1

Views

Author

Omar E. Pol, Jan 20 2009

Keywords

Crossrefs

Cf. A061357, A154720, A154724, A154725, A154726, A154786.

A154783 Row sums of triangle in A154720.

Original entry on oeis.org

1, 6, 9, 20, 15, 30, 35, 40, 63, 70, 55, 108, 65, 70, 135, 112, 119, 162, 95, 140, 231, 198, 161, 312, 225, 182, 351, 196, 203, 450, 217, 352, 429, 238, 385, 540, 407, 418, 585, 440, 369, 798, 387, 396, 945, 414, 423, 720, 441, 650, 969, 676, 583, 1026, 825, 840
Offset: 1

Views

Author

Omar E. Pol, Jan 15 2009

Keywords

Comments

Also, row sums of triangle in A154722. - Omar E. Pol, Jan 16 2009

Crossrefs

Cf. A154720, A154721, A154722, A154784, A154785, A154786.

Programs

  • Maple
    isA008578 := proc(n) RETURN(n=1 or isprime(n)) ; end: A154783 := proc(n) local a,d; a := n ; for d from 1 to n-1 do if isA008578(n-d) and isA008578(n+d) then a := a+2*n; fi; od: a ; end: for n from 1 to 80 do printf("%d,",A154783(n)) ; od: # R. J. Mathar, Jan 18 2009

Formula

a(n) = A154784(n) + n.

Extensions

Extended by R. J. Mathar, Jan 18 2009

A154784 Row sums of triangle in A154721.

Original entry on oeis.org

0, 4, 6, 16, 10, 24, 28, 32, 54, 60, 44, 96, 52, 56, 120, 96, 102, 144, 76, 120, 210, 176, 138, 288, 200, 156, 324, 168, 174, 420, 186, 320, 396, 204, 350, 504, 370, 380, 546, 400, 328, 756, 344, 352, 900, 368, 376, 672, 392, 600
Offset: 1

Views

Author

Omar E. Pol, Jan 15 2009

Keywords

Comments

a(n) is even for all n.

Links

Crossrefs

Cf. A154720, A154721, A154723, A154783, A154785, A154786.

Programs

  • Maple
    isnotcomp:=proc(n)return (n=1 or isprime(n)) end:
for n from 1 to 50 do rsum:=0: for k from 1 to 2*n-1 do if(not k=n and (isnotcomp(k) and isnotcomp(2*n-k)))then rsum:=rsum+k:fi:od: printf("%d, ",rsum):od: # Nathaniel Johnston, Apr 19 2011

Formula

a(n) = A154783(n) - n.

Extensions

Edited by Omar E. Pol, Jan 17 2009
a(11)-a(50) from Nathaniel Johnston, Apr 19 2011

A154785 Row sums of triangle in A154724.

Original entry on oeis.org

1, 2, 3, 12, 15, 18, 21, 40, 45, 50, 55, 84, 65, 70, 105, 80, 119, 162, 57, 140, 189, 154, 161, 264, 225, 182, 297, 196, 203, 390, 155, 352, 429, 170, 385, 468, 333, 418, 585, 360, 369, 714, 387, 396, 855, 414, 423, 720, 343, 650
Offset: 1

Views

Author

Omar E. Pol, Jan 15 2009

Keywords

Comments

Also, row sums of triangle in A154726.

Links

Crossrefs

Cf. A154724, A154725, A154726, A154727, A154783, A154784, A154786.

Programs

  • Maple
    for n from 1 to 50 do rsum:=0: for k from 1 to 2*n-1 do if(k=n or (isprime(k) and isprime(2*n-k)))then rsum:=rsum+k:fi:od: printf("%d, ",rsum):od: # Nathaniel Johnston, Apr 19 2011

Formula

a(n) = A154786(n) + n.

Extensions

a(11)-a(50) from Nathaniel Johnston, Apr 19 2011

A153785 5 times heptagonal numbers: a(n) = 5*n*(5*n-3)/2.

Original entry on oeis.org

0, 5, 35, 90, 170, 275, 405, 560, 740, 945, 1175, 1430, 1710, 2015, 2345, 2700, 3080, 3485, 3915, 4370, 4850, 5355, 5885, 6440, 7020, 7625, 8255, 8910, 9590, 10295, 11025, 11780, 12560, 13365, 14195, 15050, 15930, 16835, 17765
Offset: 0

Views

Author

Omar E. Pol, Jan 07 2009

Keywords

Links

Crossrefs

Cf. A000566, A153784, A154786.

Programs

  • Mathematica
    s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,5,8!,25}];lst (* Vladimir Joseph Stephan Orlovsky, Apr 03 2009 *)
Table[5*n*(5*n - 3)/2, {n,0,25}] (* or *) LinearRecurrence[{3,-3,1}, {0,5,35}, 25] (* G. C. Greubel, Aug 28 2016 *)
  • PARI
    a(n) = 5*n*(5*n-3)/2; \\ Michel Marcus, Aug 28 2016

Formula

a(n) = (25*n^2 - 15*n)/2 = A000566(n)*5.
a(n) = 25*n + a(n-1) - 20 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
From G. C. Greubel, Aug 28 2016: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: 5*x*(1 + 4*x)/(1 - x)^3.
E.g.f.: (5/2)*x*(2 + 5*x)*exp(x). (End)
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.