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

Author

David A. Corneth, Dec 30 2017

Keywords

• nonn

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

Examples

			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
		

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

Crossrefs

Cf. A055394.

Programs

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 *)

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