A188891 - OEIS

A188891

Least triangular n-gonal number greater than 1, or 0 if none exists.

3, 36, 210, 6, 55, 21, 325, 10, 0, 105, 36, 1275, 15, 45, 231, 0, 946, 276, 21, 11935, 66, 136, 351, 1596, 78, 28, 1225, 595, 820, 58653, 190, 325, 1335795, 36, 6670, 0, 561, 4005, 120, 1128, 1485, 203841, 45, 666, 6903, 465, 4950, 20910, 741, 153, 10731, 8911, 55, 1953

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OFFSET

3,1

COMMENTS

See A188893 and A188894 for the corresponding indices of these terms. Note that a(n) is zero for n = 11, 18, 38 (numbers in A188892). Although the Mathematica program searches only the first 20000 triangular numbers for n-gonal numbers, the Reduce function can show that there are no triangular n-gonal numbers (other than 0 and 1) for these n.

LINKS

Table of n, a(n) for n=3..56.

Eric W. Weisstein, MathWorld: Polygonal Number

Eric W. Weisstein, MathWorld: Triangular Number

MATHEMATICA

NgonIndex[n_, v_] := (-4 + n + Sqrt[16 - 8*n + n^2 - 16*v + 8*n*v])/(n - 2)/2; Table[k = 2; While[tr = k*(k+1)/2; i = NgonIndex[n, tr]; k < 20000 && ! IntegerQ[i], k++]; If[k==20000, tr=0]; tr, {n, 3, 50}]

Table[SelectFirst[PolygonalNumber[n, Range[2, 1000]], OddQ[Sqrt[8#+1]]&], {n, 3, 100}]/.Missing["NotFound"]->0 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 10 2019 *)

CROSSREFS

Cf. A000217 (triangular numbers), A100252 (similar sequence for squares).

Sequence in context: A168075 A275085 A303152 * A073992 A268898 A127960

Adjacent sequences: A188888 A188889 A188890 * A188892 A188893 A188894

KEYWORD

nonn

AUTHOR

T. D. Noe, Apr 13 2011

STATUS

approved