|
%I #18 Feb 01 2021 22:09:52
%S 1,3,6,10,55,66,120,153,171,190,300,351,595,630,666,820,1081,1431,
%T 1711,1891,3003,3403,5050,5460,5565,5995,6216,6786,8128,8778,10011,
%U 10731,11781,12561,13041,13861,15051,15931,16471,17020,17391,17578,18721
%N Triangular numbers with property that swapping first and last digits also gives a triangular number.
%C 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
%H Harvey P. Dale, <a href="/A069708/b069708.txt">Table of n, a(n) for n = 1..1000</a>
%e 820 and 028 = 28 both are triangular numbers hence both are members.
%t 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}]
%t 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 *)
%Y Cf. A069706, A069707.
%K nonn,base
%O 1,2
%A _Amarnath Murthy_, Apr 08 2002
%E Edited, corrected and extended by _Robert G. Wilson v_
%E Edited by _N. J. A. Sloane_, Jan 20 2009
|
