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

Author

Amarnath Murthy, Apr 08 2002

Keywords

• nonn
• base

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

Examples

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

Links

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

Crossrefs

Cf. A069706, A069707.

Programs

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 *)

Extensions

Edited, corrected and extended by Robert G. Wilson v

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