A329807 Numbers k such that k, k+1, k+2 and k+3 are all sums of a positive square and a positive cube.

126, 350, 8125, 12742, 19879, 29240, 42974, 76728, 91329, 109241, 140750, 209222, 254681, 258272, 297423, 482958, 744901, 755169, 918601, 986174, 1026214, 1418606, 1515227, 1521233, 1888216, 2082977, 2216080, 2317257, 3510926, 4180848, 4316417, 4330888, 4836895

Offset

1,1

Comments

It is known that there are infinitely many k such that k, k+1, k+2 are all sums of a positive square and a positive cube (see A055394 and A295787). It is natural to ask if this sequence is infinite. There are 243 members here below 10^9.

There are 2 pairs of consecutive numbers below 10^9: (16597502, 16597503) and (593825496, 593825497). Are there infinitely many k such that k, k+1, k+2, k+3 and k+4 are all sums of a positive square and a positive cube?

Links

Jianing Song, Table of n, a(n) for n = 1..243 (All terms <= 10^9)

Example

350 is here because 350 = 15^2 + 5^3, 351 = 18^2 + 3^3, 352 = 3^2 + 7^3 and 353 = 17^3 + 4^3.

Prog

(PARI) isA329807(n) = is(n)&&is(n+1)&&is(n+2)&&is(n+3) \\ is() is defined in A055394.

Crossrefs

Cf. A055394, A329808, A295787.

Sequence in context: A063334 A181262 A181255 * A322542 A323759 A102805

Adjacent sequences: A329804 A329805 A329806 * A329808 A329809 A329810

Keyword

nonn

Author

Jianing Song, Nov 21 2019

Status

approved