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 1-10 of 16 results. Next

A118280 Conjectured largest number that is not the sum of three (2n+1)-gonal numbers; bisection of A118278.

Original entry on oeis.org

0, 33066, 273118, 1274522, 3613278, 7250758, 12911636, 22655394, 25049533, 56922533, 81539010, 85105105, 106555658, 233296317, 286763923, 358322750
Offset: 1

Views

Author

T. D. Noe, Apr 21 2006

Keywords

Crossrefs

Cf. A118278-A118285.

Extensions

a(11)-a(16) from Donovan Johnson, Apr 17 2010

A003679 Numbers that are not the sum of 3 pentagonal numbers.

Original entry on oeis.org

4, 8, 9, 16, 19, 20, 21, 26, 30, 31, 33, 38, 42, 43, 50, 54, 55, 60, 65, 67, 77, 81, 84, 88, 89, 90, 96, 99, 100, 101, 111, 112, 113, 120, 125, 131, 135, 138, 142, 154, 159, 160, 166, 170, 171, 183, 195, 204, 205, 207, 217, 224, 225, 226, 229, 230, 236, 240, 241
Offset: 1

Views

Author

N. J. A. Sloane, Mira Bernstein

Keywords

Comments

Guy's paper says that the sequence probably contains exactly 210 terms, six of which require five pentagonal numbers: 9, 21, 31, 43, 55 and 89. The last term is conjectured to be 33066. - T. D. Noe, Apr 19 2006
The next term, if it exists, is greater than 160000000. - Jack W Grahl, Jul 10 2018
a(211) > 10^11, if it exists. - Giovanni Resta, Jul 13 2018

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A117065 (primes in this sequence).
Cf. A118278, A118279.

Programs

  • Mathematica
    nn=200; pen=Table[n(3n-1)/2, {n,0,nn-1}]; lst=Range[pen[[ -1]]; Do[n=pen[[i]]+pen[[j]]+pen[[k]]; If[n<=pen[[ -1]], lst=DeleteCases[lst,n]]], {i,nn}, {j,i,nn}, {k,j,nn}]; lst (* T. D. Noe, Apr 19 2006 *)

A118279 Conjectured number of numbers that are not the sum of three n-gonal numbers, or -1 if infinite.

Original entry on oeis.org

0, -1, 210, 638, 1348, -1, 5282, 7687, 12453, -1, 24813, -1, 45338, -1, 63702, 84764, 109613, -1, 162687, 155879, 224244, -1, 303049, -1, 353690, -1, 522262, 541796, 651844, -1, 817053
Offset: 3

Views

Author

T. D. Noe, Apr 21 2006

Keywords

Comments

See A118278 for the conjectured largest number that is not the sum of three n-gonal numbers.

Crossrefs

Cf. A118278-A118285.

Extensions

a(22)-a(33) from Donovan Johnson, Apr 17 2010

A118285 Conjectured number of numbers that are not the sum of three generalized (2n+1)-gonal numbers; bisection of A118283.

Original entry on oeis.org

0, 0, 4, 26, 94, 196, 370, 641, 999, 1537, 2619
Offset: 1

Views

Author

T. D. Noe, Apr 21 2006

Keywords

Crossrefs

Cf. A118278-A118285.

A007536 Numbers that are not the sum of 3 hexagonal numbers (probably finite).

Original entry on oeis.org

4, 5, 9, 10, 11, 14, 19, 20, 23, 24, 25, 26, 32, 33, 37, 38, 39, 41, 42, 48, 50, 53, 54, 55, 59, 63, 64, 65, 69, 70, 76, 77, 80, 83, 85, 86, 89, 99, 102, 104, 108, 110, 113, 114, 115, 116, 123, 124, 128, 129, 130, 131, 140, 143, 144, 145, 146, 152, 161, 162, 167
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Jud McCranie remarks that a(638) = 146858 is probably the last term.

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A000384 (hexagonal numbers).
Cf. A118278, A118279.

Programs

  • MATLAB
    N = 10^7; % to get all terms up to N
M = floor((sqrt(1+8*N)+1)/4);
H = zeros(1,N);
H((1:M) .*(2*(1:M)-1)) = 1;
H2 = conv(H,H);
H2 = H2(1:N);
H3 = conv(H,H2);
HS = H(3:N) + H2(2:N-1) + H3(1:N-2);
find(HS==0) + 2 % Robert Israel, Jul 06 2016
  • Mathematica
    notSumQ[n_] := Reduce[0 <= x <= y <= z && n == x*(2x - 1) + y*(2y - 1) + z*(2z - 1), {x, y, z}, Integers] === False; A007536 = Reap[ Do[ If[notSumQ[n], Print[n]; Sow[n]], {n, 1, 135}]][[2, 1]] (* Jean-François Alcover, Jun 27 2012 *)

Extensions

Corrected by T. D. Noe, Feb 14 2007

A118282 Conjectured largest number that is not the sum of three generalized n-gonal numbers, or -1 if there is no largest number.

Original entry on oeis.org

0, -1, 0, 0, 307, -1, 2027, 5200, 18180, -1, 10795, -1, 87740, -1, 75150, 212048, 122818, -1, 146970, 199153, 585513
Offset: 3

Views

Author

T. D. Noe, Apr 21 2006

Keywords

Comments

Extensive calculations show that if a(n)>=0, then every number greater than a(n) can be represented as the sum of three generalized n-gonal numbers. a(n)=0 for n=3 and 6 because generalized triangular and generalized hexagonal numbers are the same a triangular numbers and every number can be written as the sum of three triangular numbers. When n is a multiple of 4, there is an infinite set of numbers not representable. For n=14, there appears to be a sparse, but infinite, set of numbers not representable. See A118283 for the number of numbers not representable.

Crossrefs

Cf. A001318 (generalized pentagonal numbers), A085787 (generalized heptagonal numbers), A001082 (generalized octagonal numbers), A118277 (generalized 9-gonal numbers), A118278-A118285.

A213523 Numbers not representable as the sum of three heptagonal numbers.

Original entry on oeis.org

4, 5, 6, 10, 11, 12, 13, 16, 17, 22, 23, 24, 27, 28, 29, 30, 31, 33, 38, 39, 40, 44, 45, 46, 47, 49, 50, 51, 58, 60, 61, 64, 65, 66, 67, 71, 72, 76, 77, 78, 79, 84, 85, 87, 92, 93, 94, 97, 98, 101, 103, 104, 105, 108, 109, 118, 121, 124, 125, 127, 129, 132
Offset: 1

Views

Author

T. D. Noe, Jul 16 2012

Keywords

Comments

It is conjectured that 1348 positive numbers are not the sum of three heptagonal numbers.

References

  • R. K. Guy, Unsolved Problems in Number Theory, D3.

Links

Crossrefs

Cf. A000566 (heptagonal numbers).
Cf. A118278, A118279.

Programs

  • Mathematica
    nn = 350; hep = Table[n*(5*n-3)/2, {n, 0, nn}]; t = Table[0, {hep[[-1]]}]; Do[n = hep[[i]] + hep[[j]] + hep[[k]]; If[n <= hep[[-1]], t[[n]] = 1], {i, nn}, {j, i, nn}, {k, j, nn}]; Flatten[Position[t, 0]]

A118283 Conjectured number of numbers that are not the sum of three generalized n-gonal numbers, or -1 if infinite.

Original entry on oeis.org

0, -1, 0, 0, 4, -1, 26, 45, 94, -1, 196, -1, 370, -1, 641, 743, 999, -1, 1537, 1429, 2619
Offset: 3

Views

Author

T. D. Noe, Apr 21 2006

Keywords

Comments

See A118282 for the conjectured largest number that is not the sum of three generalized n-gonal numbers. For n=7, only four numbers are not representable: 10, 16, 76 and 307.

Crossrefs

Cf. A118278-A118285.

A118286 Numbers n such that n == 0 (mod 4) or n == 2 (mod 12).

Original entry on oeis.org

2, 4, 8, 12, 14, 16, 20, 24, 26, 28, 32, 36, 38, 40, 44, 48, 50, 52, 56, 60, 62, 64, 68, 72, 74, 76, 80, 84, 86, 88, 92, 96, 98, 100, 104, 108, 110, 112, 116, 120, 122, 124, 128, 132, 134, 136, 140, 144, 146, 148, 152, 156, 158, 160, 164, 168, 170, 172, 176, 180, 182
Offset: 1

Views

Author

T. D. Noe, Apr 23 2006

Keywords

Comments

Except for n=2, conjectured n such that A118278(n)=-1 and A118282(n)=-1; n such that there is an infinite set of numbers not representable as the sum of three n-gonal numbers or three generalized n-gonal numbers.
The difference between two consecutive terms follow the 4-period: (2, 4, 4, 2). - Bernard Schott, Feb 25 2019

Links

Crossrefs

Cf. A047237, A118278, A118282.

Programs

  • GAP
    Filtered([1..190],n->n mod 4=0 or n mod 12=2); # Muniru A Asiru, Feb 22 2019
  • Magma
    [Round((3*n-1) + (Sqrt(-1))^n*(1+(-1)^n)/2): n in [1..70]]; // G. C. Greubel, Feb 21 2019
  • Maple
    select(n->modp(n,4)=0 or modp(n,12)=2,[$1..190]); # Muniru A Asiru, Feb 22 2019
  • Mathematica
    Union[4*Range[50], 2+12*Range[16]]
  • PARI
    a(n) = (-2+(-I)^n+I^n+6*n)/2 \\ Colin Barker, Oct 19 2015
  • PARI
    Vec(2*x*(1+2*x^2)/((1+x^2)*(1-x)^2) + O(x^70)) \\ Colin Barker, Oct 19 2015
  • PARI
    for(n=1, 1e3, if(n%4 == 0 || n%12 == 2, print1(n", "))) \\ Altug Alkan, Oct 19 2015
  • Sage
    [(3*n-1) + I^n*(1+(-1)^n)/2 for n in (1..70)] # G. C. Greubel, Feb 21 2019

Formula

G.f.: 2*x*(1+2*x^2) / ( (1+x^2)*(1-x)^2 ). - R. J. Mathar, Dec 02 2011
a(n) = 2*A047237(n+1) = 3*n - 1 + cos(n*Pi/2). - R. J. Mathar, Dec 02 2011
a(n) = (-2 + (-i)^n + i^n + 6*n)/2, where i = sqrt(-1). - Colin Barker, Oct 19 2015
a(n) = (6*n - 2 + (1 + (-1)^n)*(-1)^(n*(n-1)/2))/2. - Guenther Schrack, Feb 21 2019
E.g.f.: cos(x) + (3*x-1)*exp(x). - G. C. Greubel, Feb 21 2019

A213524 Numbers not representable as the sum of three octagonal numbers.

Original entry on oeis.org

4, 5, 6, 7, 11, 12, 13, 14, 15, 18, 19, 20, 25, 26, 27, 28, 31, 32, 33, 34, 35, 36, 38, 39, 44, 45, 46, 47, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 68, 70, 71, 72, 75, 76, 77, 78, 79, 83, 84, 85, 89, 90, 91, 92, 93, 95, 99, 100, 102, 103, 108, 109, 110, 111
Offset: 1

Views

Author

T. D. Noe, Jul 16 2012

Keywords

Comments

There are an infinite number of numbers that are not the sum of three octagonal numbers.

References

  • R. K. Guy, Unsolved Problems in Number Theory, D3.

Links

Crossrefs

Cf. A000567 (octagonal numbers).
Cf. A118278, A118279.

Programs

  • Mathematica
    nn = 100; oct = Table[n*(3*n-2), {n, 0, nn}]; t = Table[0, {oct[[-1]]}]; Do[n = oct[[i]] + oct[[j]] + oct[[k]]; If[n <= oct[[-1]], t[[n]] = 1], {i, nn}, {j, i, nn}, {k, j, nn}]; Flatten[Position[t, 0]]
Showing 1-10 of 16 results. Next

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

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