A333007 -id:A333007 - cp's OEIS frontend

A333008 Square roots of perfect squares which are sum of two nonzero pentagonal numbers (A333007).

6, 11, 14, 20, 25, 35, 39, 59, 76, 84, 85, 92, 94, 95, 96, 104, 105, 108, 116, 123, 125, 129, 133, 136, 147, 153, 157, 160, 169, 174, 181, 186, 189, 190, 192, 194, 195, 198, 200, 206, 207, 231, 232, 238, 239, 248, 256, 270, 274, 279, 283, 288, 293, 302, 304, 307, 309, 323, 326, 332, 340, 344, 346, 350, 360, 361, 363, 370, 371, 377, 385, 391, 398, 399

Offset: 1

Olivier Gérard, Mar 05 2020

nonn

			a(7) = 39.  a(7)^2 = 1521 = 1 + 1520.

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

Cf. A333007 (squares), A333009 (successive differences).

Cf. A000326 (pentagonal numbers).

Take[Union[Select[Sqrt[#]&/@(Total/@Tuples[PolygonalNumber[ 5,Range[ 400]],2]),IntegerQ]],80] (* Harvey P. Dale, Apr 22 2022 *)

A333009 Successive differences of A333008 (square roots of perfect squares that are the sum of two nonzero pentagonal numbers).

Original entry on oeis.org

5, 3, 6, 5, 10, 4, 20, 17, 8, 1, 7, 2, 1, 1, 8, 1, 3, 8, 7, 2, 4, 4, 3, 11, 6, 4, 3, 9, 5, 7, 5, 3, 1, 2, 2, 1, 3, 2, 6, 1, 24, 1, 6, 1, 9, 8, 14, 4, 5, 4, 5, 5, 9, 2, 3, 2, 14, 3, 6, 8, 4, 2, 4, 10, 1, 2, 7, 1, 6, 8, 6, 7, 1, 8, 5, 7, 12, 8, 4, 4, 5, 2, 11, 4

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..1000

Cf. A332986 (analog for indices of triangular numbers).

Cf. A000326, A333007, A333008.

cp's OEIS Frontend

A333008 Square roots of perfect squares which are sum of two nonzero pentagonal numbers (A333007).

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