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A069708
Triangular numbers with property that swapping first and last digits also gives a triangular number.
3
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
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
Sequence in context: A048089 A081975 A160965 * A061455 A068071 A067269
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