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 10 results.

A118281 Conjectured number of numbers that are not the sum of three (2n+1)-gonal numbers; bisection of A118279.

Original entry on oeis.org

0, 210, 1348, 5282, 12453, 24813, 45338, 63702, 109613, 162687, 224244, 303049, 353690, 522262, 651844, 817053
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

A118278 Conjectured largest number that is not the sum of three n-gonal numbers, or -1 if there is no largest number.

Original entry on oeis.org

0, -1, 33066, 146858, 273118, -1, 1274522, 2117145, 3613278, -1, 7250758, -1, 12911636, -1, 22655394, 26801303, 25049533, -1, 56922533, 115715602, 81539010, -1, 85105105, -1, 106555658, -1, 233296317, 267370631, 286763923, -1, 358322750
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 n-gonal numbers. a(3)=0 because 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.

Links

Crossrefs

Cf. A118279 (number of numbers not representable).
Cf. A003679 (not the sum of three pentagonal numbers).
Cf. A007536 (not the sum of three hexagonal numbers).
Cf. A213523 (not the sum of three heptagonal numbers).
Cf. A213524 (not the sum of three octagonal numbers).
Cf. A213525 (not the sum of three 9-gonal numbers).
Cf. A214419 (not the sum of three 10-gonal numbers).
Cf. A214420 (not the sum of three 11-gonal numbers).
Cf. A214421 (not the sum of three 12-gonal numbers).

Extensions

a(22)-a(33) 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 *)

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

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]]

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]]

A213525 Numbers not representable as the sum of three 9-gonal numbers.

Original entry on oeis.org

4, 5, 6, 7, 8, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 50, 51, 52, 53, 54, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 73, 74, 78, 80, 81, 82, 83, 86, 87, 88, 89, 90, 91, 95, 96, 97, 98, 102, 103
Offset: 1

Views

Author

T. D. Noe, Jul 16 2012

Keywords

Comments

It is conjectured that 5282 positive numbers are not the sum of three 9-gonal numbers.

References

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

Links

Crossrefs

Cf. A001106 (9-gonal numbers).
Cf. A118278, A118279.

Programs

  • Mathematica
    nn = 700; non = Table[n*(7*n - 5)/2, {n, 0, nn}]; t = Table[0, {non[[-1]]}]; Do[n = non[[i]] + non[[j]] + non[[k]]; If[n <= non[[-1]], t[[n]] = 1], {i, nn}, {j, i, nn}, {k, j, nn}]; Flatten[Position[t, 0]]

A214419 Numbers not representable as the sum of three 10-gonal numbers.

Original entry on oeis.org

4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 56, 57, 58, 59, 60, 61, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 82, 83, 84, 88, 90, 91, 92, 93, 94, 97, 98
Offset: 1

Views

Author

T. D. Noe, Jul 17 2012

Keywords

Comments

It is conjectured that 7687 positive numbers are not the sum of three 10-gonal numbers.

References

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

Links

Crossrefs

Cf. A001107 (10-gonal numbers).
Cf. A118278, A118279.

Programs

  • Mathematica
    nn = 750; dec = Table[n*(4*n-3), {n, 0, nn}]; t = Table[0, {dec[[-1]]}]; Do[n = dec[[i]] + dec[[j]] + dec[[k]]; If[n <= dec[[-1]], t[[n]] = 1], {i, nn}, {j, i, nn}, {k, j, nn}]; Flatten[Position[t, 0]]

A214420 Numbers not representable as the sum of three 11-gonal numbers.

Original entry on oeis.org

4, 5, 6, 7, 8, 9, 10, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25, 26, 27, 28, 29, 34, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 62, 63, 64, 65, 66, 67, 68, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 91, 92
Offset: 1

Views

Author

T. D. Noe, Jul 17 2012

Keywords

Comments

It is conjectured that 12453 positive numbers are not the sum of three 11-gonal numbers.

References

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

Links

Crossrefs

Cf. A051682 (11-gonal numbers).
Cf. A118278, A118279.

Programs

  • Mathematica
    nn = 900; hen = Table[n*(9*n-7)/2, {n, 0, nn}]; t = Table[0, {hen[[-1]]}]; Do[n = hen[[i]] + hen[[j]] + hen[[k]]; If[n <= hen[[-1]], t[[n]] = 1], {i, nn}, {j, i, nn}, {k, j, nn}]; Flatten[Position[t, 0]]

A214421 Numbers not representable as the sum of three 12-gonal numbers.

Original entry on oeis.org

4, 5, 6, 7, 8, 9, 10, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 27, 28, 29, 30, 31, 32, 37, 38, 39, 40, 41, 42, 43, 44, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 68, 69, 70, 71, 72, 73, 74, 75, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89
Offset: 1

Views

Author

T. D. Noe, Jul 17 2012

Keywords

Comments

There are an infinite number of numbers that are not the sum of three 12-gonal numbers.

References

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

Links

Crossrefs

Cf. A051624 (12-gonal numbers).
Cf. A118278, A118279.

Programs

  • Mathematica
    nn = 100; dod = Table[n*(5n-4), {n, 0, nn}]; t = Table[0, {dod[[-1]]}]; Do[n = dod[[i]] + dod[[j]] + dod[[k]]; If[n <= dod[[-1]], t[[n]] = 1], {i, nn}, {j, i, nn}, {k, j, nn}]; Flatten[Position[t, 0]]
Showing 1-10 of 10 results.

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

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