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A329807
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Numbers k such that k, k+1, k+2 and k+3 are all sums of a positive square and a positive cube.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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?
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LINKS
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EXAMPLE
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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.
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PROG
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(PARI) isA329807(n) = is(n)&&is(n+1)&&is(n+2)&&is(n+3) \\ is() is defined in A055394.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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