A069708 Triangular numbers with property that swapping first and last digits also gives a triangular number.

1, 3, 6, 10, 55, 66, 120, 153, 171, 190, 300, 351, 595, 630, 666, 820, 1081, 1431, 1711, 1891, 3003, 3403, 5050, 5460, 5565, 5995, 6216, 6786, 8128, 8778, 10011, 10731, 11781, 12561, 13041, 13861, 15051, 15931, 16471, 17020, 17391, 17578, 18721

Offset

1,2

Comments

934 of the first 1000 terms begin and end with the same digit. 40 of the first 1000 terms end in zero. Thus, only 26 of the first 1000 terms begin and end with different nonzero digits, with 153 being the smallest and 8026021 being the largest of those terms. - Harvey P. Dale, Jan 09 2021

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

820 and 028 = 28 both are triangular numbers hence both are members.

Mathematica

Do[t = IntegerDigits[n(n + 1)/2]; u = t; u[[1]] = t[[ -1]]; u[[ -1]] = t[[1]]; t = FromDigits[u]; u = Floor[ Sqrt[2t]]; If[ u(u + 1)/2 == t, Print[n(n + 1)/2]], {n, 1, 300}]
sfl[n_]:=Module[{idn=IntegerDigits[n]}, FromDigits[Flatten[Join[{Last[ idn], Rest[ Most[ idn]], First[ idn]}]]]]; Join[ {1, 3, 6}, Select[ Accumulate[ Range[200]], OddQ[Sqrt[8 sfl[#]+1]]&]//Quiet] (* Harvey P. Dale, Jan 09 2021 *)

Crossrefs

Cf. A069706, A069707.

Sequence in context: A048089 A081975 A160965 * A061455 A068071 A067269

Adjacent sequences: A069705 A069706 A069707 * A069709 A069710 A069711

Keyword

nonn,base

Author

Amarnath Murthy, Apr 08 2002

Extensions

Edited, corrected and extended by Robert G. Wilson v

Edited by N. J. A. Sloane, Jan 20 2009

Status

approved