A115677 Brilliant numbers (A078972) whose digit reversal is a triangular number.
6, 10, 649, 1207, 54253, 56341, 60391, 66259, 66331, 101971, 155143, 166339, 351433, 672319, 3003193, 3054853, 5043763, 5631229, 5858119, 6163831, 6256603, 6462847, 6473899, 6556177, 6687883, 8210989, 8236513, 8735491, 8788033, 10716571, 11576143
Offset: 1
Examples
649=11*59 is brilliant and 946=T(43).
Programs
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Mathematica
bnoQ[n_]:=Module[{fi=FactorInteger[n],tfi,nn}, tfi=Transpose[fi]; Total[tfi[[2]]]==2 &&IntegerLength[First[tfi[[1]]]] == IntegerLength[Last[tfi[[1]]]]]; tnoQ[n_]:=IntegerQ[(Sqrt[1 +8FromDigits[ Reverse[IntegerDigits[n]]]]-1)/2]; Select[Select[Range[700000], bnoQ], tnoQ] (* Harvey P. Dale, Apr 17 2011 *)
Extensions
a(15)-a(31) from Donovan Johnson, Apr 26 2011