A102795 -id:A102795 - cp's OEIS frontend

A102801 Let f(n) be the minimal number of distinct nonzero tetrahedral numbers that add to n (or -1 if n is not a sum of distinct tetrahedral numbers); sequence gives numbers n for which f(n) = 2.

5, 11, 14, 21, 24, 30, 36, 39, 45, 55, 57, 60, 66, 76, 85, 88, 91, 94, 104, 119, 121, 124, 130, 140, 155, 166, 169, 175, 176, 185, 200, 204, 221, 224, 230, 240, 249, 255, 276, 285, 287, 290, 296, 304, 306, 321, 340, 342, 365, 368, 370, 374, 384

Offset: 1

Jud McCranie, Feb 26 2005

nonn

			680 (of A034404) is a sum of two distinct positive tetrahedral numbers but not in the list because it is also a tetrahedral number itself. - _R. J. Mathar_, Jun 05 2025

R. J. Mathar, Table of n, a(n) for n = 1..966

Cf. A000292, A104246, A102795, etc.

A288631 Numbers that are the sum of two nonzero square pyramidal numbers (A000330).

Original entry on oeis.org

2, 6, 10, 15, 19, 28, 31, 35, 44, 56, 60, 69, 85, 92, 96, 105, 110, 121, 141, 145, 146, 154, 170, 182, 195, 205, 209, 218, 231, 234, 259, 280, 286, 290, 295, 299, 315, 340, 344, 376, 386, 390, 399, 408, 415, 425, 440, 476, 489, 507, 511, 520, 525, 536, 561, 570, 589, 597, 646, 651, 655, 664, 670, 680

Offset: 1

Ilya Gutkovskiy, Jun 12 2017

nonn

Robert Israel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Square Pyramidal Number
Index to sequences related to pyramidal numbers

Cf. A000330, A000404, A020756, A051533, A102795.

M:= 20: # to get all terms <= A000330(M)
sqp:= [seq(k*(k+1)*(2*k+1)/6, k=1..M)]:
sort(convert(select(`<=`, {seq(seq(sqp[i]+sqp[j], j=1..i),i=1..M-1)},sqp[M]),list)); # Robert Israel, Jun 12 2017

nmax = 700; f[x_] := Sum[x^(k (k + 1) (2 k + 1)/6), {k, 1, 20}]^2; Exponent[#, x] & /@ List @@ Normal[Series[f[x], {x, 0, nmax}]]

A102800 Let f(n) = A104246(n) be the minimal number of nonzero tetrahedral numbers that add to n; sequence gives numbers n for which f(n) <= 4.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74

Offset: 1

Jud McCranie, Feb 26 2005

nonn

Cf. A000292, A000797, A104246, A102795, etc.

A102802 Let f(n) be the minimal number of distinct nonzero tetrahedral numbers that add to n (or -1 if n is not a sum of distinct tetrahedral numbers); sequence gives numbers n for which f(n) = 3.

Original entry on oeis.org

15, 25, 31, 34, 40, 46, 49, 59, 61, 65, 67, 70, 77, 80, 86, 89, 92, 95, 98, 101, 105, 108, 111, 114, 123, 125, 129, 131, 134, 139, 141, 144, 150, 156, 159, 160, 170, 177, 179, 180, 186, 189, 195, 196, 201, 205, 208, 210, 211, 214, 222, 225, 231

Offset: 1

Jud McCranie, Feb 26 2005

nonn

Cf. A000292, A104246, A102795, etc.

A287960 Numbers that are the sum of two centered triangular numbers (A005448).

Original entry on oeis.org

2, 5, 8, 11, 14, 20, 23, 29, 32, 35, 38, 41, 47, 50, 56, 62, 65, 68, 74, 77, 83, 86, 89, 92, 95, 104, 110, 113, 116, 119, 128, 131, 137, 140, 146, 149, 155, 167, 170, 173, 176, 182, 185, 194, 197, 200, 203, 209, 212, 218, 221, 230, 236, 239, 245, 251, 254, 263, 266, 272, 275, 278, 281, 284, 293, 299

Offset: 1

Ilya Gutkovskiy, Jun 03 2017

nonn

Eric Weisstein's World of Mathematics, Centered Triangular Number
Index entries for sequences related to centered polygonal numbers

Cf. A005448, A020756, A051533, A102795, A286636.

nmax = 300; f[x_] := Sum[x^(3 k (k - 1)/2 + 1), {k, 1, 20}]^2; Exponent[#, x] & /@ List @@ Normal[Series[f[x], {x, 0, nmax}]]

8*a(n) = 10+3*A097269(n). - R. J. Mathar, Jul 26 2017

A102799 Let f(n) = A104246(n) be the minimal number of nonzero tetrahedral numbers that add to n; sequence gives numbers n for which f(n) <= 3.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 18, 20, 21, 22, 24, 25, 28, 30, 31, 34, 35, 36, 37, 39, 40, 41, 43, 44, 45, 46, 49, 50, 55, 56, 57, 58, 59, 60, 61, 64, 65, 66, 67, 70, 71, 74, 75, 76, 77, 80, 84, 85, 86, 88, 89, 90, 91, 92, 94, 95, 96, 98, 101, 104, 105

Offset: 1

Jud McCranie, Feb 26 2005

nonn

Cf. A000292, A104246, A102795, etc.

A102803 Let f(n) be the minimal number of distinct nonzero tetrahedral numbers that add to n (or -1 if n is not a sum of distinct tetrahedral numbers); sequence gives numbers n for which f(n) = 4.

Original entry on oeis.org

50, 69, 71, 81, 87, 90, 96, 99, 102, 109, 112, 115, 118, 133, 135, 143, 145, 149, 151, 154, 161, 164, 181, 187, 190, 197, 199, 206, 209, 212, 215, 218, 226, 228, 232, 235, 242, 243, 245, 251, 254, 257, 261, 263, 264, 266, 270, 273, 279, 281

Offset: 1

Jud McCranie, Feb 26 2005

nonn

Cf. A000292, A104246, A102795, etc.

A102804 Let f(n) be the minimal number of distinct nonzero tetrahedral numbers that add to n (or -1 if n is not a sum of distinct tetrahedral numbers); sequence gives numbers n for which f(n) = 5.

Original entry on oeis.org

106, 116, 122, 153, 171, 174, 191, 207, 216, 219, 229, 236, 238, 246, 252, 267, 271, 274, 283, 298, 319, 329, 336, 338, 355, 357, 367, 382, 383, 393, 401, 408, 414, 432, 433, 435, 437, 438, 447, 454, 467, 474, 477, 492, 499, 513, 518, 528

Offset: 1

Jud McCranie, Feb 26 2005

nonn

Cf. A000292, A104246, A102795, etc.

A102805 Let f(n) be the minimal number of distinct nonzero tetrahedral numbers that add to n (or -1 if n is not a sum of distinct tetrahedral numbers); sequence gives numbers n for which f(n) = 6.

Original entry on oeis.org

126, 392, 402, 418, 439, 457, 464, 502, 538, 577, 587, 602, 612, 638, 657, 722, 793, 812, 822, 838, 863, 1007, 1062, 1198, 1408, 1423

Offset: 1

Jud McCranie, Feb 26 2005

nonn

It appears that there are just two numbers n for which f(n) = 7, namely 412 and 622 and none with f(n) > 7.

Cf. A000292, A104246, A102795, etc.

cp's OEIS Frontend

A102801 Let f(n) be the minimal number of distinct nonzero tetrahedral numbers that add to n (or -1 if n is not a sum of distinct tetrahedral numbers); sequence gives numbers n for which f(n) = 2.

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A288631 Numbers that are the sum of two nonzero square pyramidal numbers (A000330).

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A102800 Let f(n) = A104246(n) be the minimal number of nonzero tetrahedral numbers that add to n; sequence gives numbers n for which f(n) <= 4.

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A102802 Let f(n) be the minimal number of distinct nonzero tetrahedral numbers that add to n (or -1 if n is not a sum of distinct tetrahedral numbers); sequence gives numbers n for which f(n) = 3.

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A287960 Numbers that are the sum of two centered triangular numbers (A005448).

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Mathematica

Formula

A102799 Let f(n) = A104246(n) be the minimal number of nonzero tetrahedral numbers that add to n; sequence gives numbers n for which f(n) <= 3.

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A102803 Let f(n) be the minimal number of distinct nonzero tetrahedral numbers that add to n (or -1 if n is not a sum of distinct tetrahedral numbers); sequence gives numbers n for which f(n) = 4.

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Crossrefs

A102804 Let f(n) be the minimal number of distinct nonzero tetrahedral numbers that add to n (or -1 if n is not a sum of distinct tetrahedral numbers); sequence gives numbers n for which f(n) = 5.

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Author

Keywords

Crossrefs

A102805 Let f(n) be the minimal number of distinct nonzero tetrahedral numbers that add to n (or -1 if n is not a sum of distinct tetrahedral numbers); sequence gives numbers n for which f(n) = 6.

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