A233473 Least k such that there are n triangular numbers between triangular(k) and k^2.

0, 4, 7, 9, 11, 14, 16, 19, 21, 23, 26, 28, 31, 33, 36, 38, 40, 43, 45, 48, 50, 52, 55, 57, 60, 62, 64, 67, 69, 72, 74, 77, 79, 81, 84, 86, 89, 91, 93, 96, 98, 101, 103, 106, 108, 110, 113, 115, 118, 120, 122, 125, 127, 130, 132, 134, 137, 139, 142, 144, 147

Offset

0,2

Links

Table of n, a(n) for n=0..60.

Example

Least k such that there are 2 triangular numbers between triangular(k) and k^2 is k=7: triangular(8)=36 and triangular(9)=45 are between triangular(7)=28 and 7^2=49. Thus a(2)=7.
Least k such that there are 3 triangular numbers between triangular(k) and k^2 is k=9: 55, 66, 78 are the triangular numbers between triangular(9)=45 and 9^2=81. Thus a(3)=9.

Mathematica

nn = 1000; tri = Table[n*(n+1)/2, {n, 0, Sqrt[2]*nn}]; sq = Range[nn]^2; t = Table[Length[Select[tri, tri[[n]] < # < sq[[n]] &]], {n, nn}]; Join[{0}, Table[Position[t, n, 1, 1][[1, 1]], {n, Max[t]}]] (* T. D. Noe, Dec 13 2013 *)

Crossrefs

Cf. A000217, A000290.

Sequence in context: A310946 A265140 A288510 * A109180 A025054 A310947

Adjacent sequences: A233470 A233471 A233472 * A233474 A233475 A233476

Keyword

nonn

Author

Alex Ratushnyak, Dec 11 2013

Status

approved