A295787 Positive integers m such that m, m + 1 and m + 2 are a sum of a positive square and a positive cube.

126, 127, 350, 351, 441, 485, 511, 848, 1431, 1568, 2024, 2752, 2843, 3024, 3844, 4697, 5489, 7120, 7343, 7399, 8125, 8126, 8623, 9430, 9800, 10703, 10842, 11474, 12176, 12335, 12742, 12743, 13748, 14191, 14911, 15254, 16128, 16640, 16857, 17067, 17207, 18095, 18567

Offset

1,1

Comments

Is a(n) >= c*n^e for some constants c and e? For terms in the b-file, we'd have e > 2.1598. - David A. Corneth, Mar 15 2019

Links

David A. Corneth, Table of n, a(n) for n = 1..14685 (Terms <= 10^9)

Bundeswettbewerb Mathematik 2017, Die Aufgaben der 2. Runde 2017

Bundeswettbewerb Mathematik 2017, Aufgaben und Lösungen 2. Runde 2017

David A. Corneth, PARI program

Example

126 and 127 are terms because: 126 = 1^2 + 5^3, 127 = 10^2 + 3^3, 128 = 8^2 + 4^3, 129 = 11^2 + 2^3. - Bernard Schott, Mar 17 2019

Mathematica

s = Union@ Flatten@ Table[s^2 + c^3, {s, 141}, {c, 27}]; First@# & /@ Select[Partition[s, 3, 1], #[[1]] + 2 == #[[3]] &] (* Robert G. Wilson v, Jan 07 2018 *)
With[{mx=19000}, Select[Partition[Union[Flatten[Table[a^2+b^3, {a, Ceiling[ Sqrt[mx]]}, {b, Ceiling[Surd[mx, 3]]}]]], 3, 1], Differences[#]=={1, 1}&]][[All, 1]] (* Harvey P. Dale, Sep 07 2020 *)

Prog

(PARI) is_a055394(n) = for(k=1, sqrtnint(n-1, 3), if(issquare(n-k^3), return(1))); 0 \\ after Charles R Greathouse IV
is(n) = is_a055394(n) && is_a055394(n+1) && is_a055394(n+2) \\ Felix Fröhlich, Jan 08 2018
(PARI) See Corneth Link \\ David A. Corneth, Mar 15 2019

Crossrefs

Cf. A055394.

Sequence in context: A100730 A044876 A080539 * A308534 A045167 A216063

Adjacent sequences: A295784 A295785 A295786 * A295788 A295789 A295790

Keyword

nonn

Author

David A. Corneth, Dec 30 2017

Status

approved