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A329807 Numbers k such that k, k+1, k+2 and k+3 are all sums of a positive square and a positive cube. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A055934 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

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Last modified December 7 14:20 EST 2022. Contains 358656 sequences. (Running on oeis4.)