A332987 -id:A332987 - cp's OEIS frontend

A332988 Sums of two distinct nonzero pentagonal numbers.

6, 13, 17, 23, 27, 34, 36, 40, 47, 52, 56, 57, 63, 71, 73, 75, 82, 86, 92, 93, 97, 104, 105, 114, 118, 121, 122, 127, 129, 139, 143, 146, 150, 152, 157, 162, 167, 168, 177, 180, 181, 187, 188, 196, 198, 209, 211, 215, 222, 227, 232, 237, 245, 246, 248, 252, 259, 261, 262, 268, 269, 280, 282, 288, 292, 293, 298, 299, 302, 309, 317, 321, 322, 327, 331, 335, 338, 339, 342, 352, 355, 357, 364, 365, 377, 379, 381, 386, 388, 392, 398

Offset: 1

Olivier Gérard, Mar 05 2020

A subset of A332987.

Cf. A000326 (pentagonal numbers).

Total/@Subsets[PolygonalNumber[5,Range[20]],{2}]//Union (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 22 2020 *)

A333007 Perfect squares that are sum of two nonzero pentagonal numbers.

Original entry on oeis.org

36, 121, 196, 400, 625, 1225, 1521, 3481, 5776, 7056, 7225, 8464, 8836, 9025, 9216, 10816, 11025, 11664, 13456, 15129, 15625, 16641, 17689, 18496, 21609, 23409, 24649, 25600, 28561, 30276, 32761, 34596, 35721, 36100, 36864, 37636, 38025, 39204, 40000, 42436, 42849

Offset: 1

Olivier Gérard, Mar 05 2020

			36  = 6^2  = 1  + 35;
121 = 11^2 = 51 + 70;
196 = 14^2 = 51 + 145.

Peter Kagey, Table of n, a(n) for n = 1..1000

Cf. A000326, A332987, A332988, A333008, A333009.

is(k) = issquare(k) && sum(i=1, sqrt(1+12*k)\6, sqrt(1+24*k+12*i-36*i*i)%6==5)>0; \\ Jinyuan Wang, Mar 06 2020

More terms from Jinyuan Wang, Mar 06 2020

A332984 Triangular numbers also sum of two nonzero pentagonal numbers.

Original entry on oeis.org

6, 10, 36, 105, 528, 595, 861, 903, 1081, 1128, 1225, 1431, 1711, 2016, 2211, 2278, 2415, 2556, 2926, 3160, 3403, 3741, 4005, 4095, 5050, 5151, 5253, 6105, 6441, 6903, 7750, 8385, 10011, 11476, 12720, 14196, 15400, 15931, 16836, 17391, 18528, 19110

Offset: 1

Olivier Gérard, Mar 05 2020

			    6 =  1 +  5;
   10 =  5 +  5;
   36 =  1 + 35;
  105 = 35 + 70.

Peter Kagey, Table of n, a(n) for n = 1..1000

A subset of A000217 (triangular numbers) and of A332987 (sums of two nonzero pentagonal numbers).

Cf. A000326 (pentagonal numbers).

A332985 Index of triangular numbers that are sum of two pentagonal numbers (A332984).

Original entry on oeis.org

3, 4, 8, 14, 32, 34, 41, 42, 46, 47, 49, 53, 58, 63, 66, 67, 69, 71, 76, 79, 82, 86, 89, 90, 100, 101, 102, 110, 113, 117, 124, 129, 141, 151, 159, 168, 175, 178, 183, 186, 192, 195, 205, 216, 217, 219, 232, 241, 247, 250, 252, 253, 255, 258, 261, 263, 265, 271, 284, 293, 297, 298

Offset: 1

Olivier Gérard, Mar 05 2020

The index of a triangular number T is the integer n such that T = n*(n+1)/2.

Peter Kagey, Table of n, a(n) for n = 1..1000

Cf. A000217 (triangular numbers), A000326 (pentagonal numbers), A332987 (sums of two nonzero pentagonal numbers).

A332986 Successive differences of index of triangular numbers sum of two pentagonal numbers.

Original entry on oeis.org

1, 4, 6, 18, 2, 7, 1, 4, 1, 2, 4, 5, 5, 3, 1, 2, 2, 5, 3, 3, 4, 3, 1, 10, 1, 1, 8, 3, 4, 7, 5, 12, 10, 8, 9, 7, 3, 5, 3, 6, 3, 10, 11, 1, 2, 13, 9, 6, 3, 2, 1, 2, 3, 3, 2, 2, 6, 13, 9, 4, 1, 11, 1, 3, 8, 9, 1, 4, 6, 3, 8, 3, 5, 2, 3, 2, 5, 1, 14, 9

Offset: 1

Olivier Gérard, Mar 05 2020

nonn

The behavior of this sequence is unexpectedly quite complex.

Peter Kagey, Table of n, a(n) for n = 1..2500

Cf. A000217 (triangular numbers), A000326 (pentagonal numbers), A332987 (sums of two nonzero pentagonal numbers), A333009 (analog for indices of square numbers).

Cf. First differences of A332985.

A330031 Sums of two nonzero tetrahedral numbers (A000292).

Original entry on oeis.org

2, 5, 8, 11, 14, 20, 21, 24, 30, 36, 39, 40, 45, 55, 57, 60, 66, 70, 76, 85, 88, 91, 94, 104, 112, 119, 121, 124, 130, 140, 155, 166, 168, 169, 175, 176, 185, 200, 204, 221, 224, 230, 240, 249, 255, 276, 285, 287, 290, 296, 304, 306, 321, 330, 340, 342, 365

Offset: 1

Peter Kagey, Mar 07 2020

nonn

Peter Kagey, Table of n, a(n) for n = 1..10000

Cf. A000292, A102798, A104246.

Analogs for other figurate numbers are A000404 (squares), A003325 (cubes), A051533 (triangular numbers), A286636 (centered square numbers), A287960 (centered triangular numbers), A288631 (square pyramidal numbers), A332987 (pentagonal numbers).

cp's OEIS Frontend

A332988 Sums of two distinct nonzero pentagonal numbers.

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A333007 Perfect squares that are sum of two nonzero pentagonal numbers.

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A332984 Triangular numbers also sum of two nonzero pentagonal numbers.

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A332985 Index of triangular numbers that are sum of two pentagonal numbers (A332984).

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A332986 Successive differences of index of triangular numbers sum of two pentagonal numbers.

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A330031 Sums of two nonzero tetrahedral numbers (A000292).

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