A077671 Triangular numbers whose digit permutations yield at least one further triangular number.

10, 105, 120, 153, 190, 210, 253, 300, 325, 351, 496, 630, 780, 820, 946, 1035, 1378, 1485, 1830, 1891, 2080, 2145, 2415, 2701, 2850, 3081, 3160, 3570, 3655, 3741, 3916, 4005, 4095, 4371, 4560, 4851, 4950, 5050, 5356, 5460, 5565, 5778, 6105, 6555, 7021

Offset: 1

Author

Amarnath Murthy, Nov 16 2002

Keywords

• nonn
• base

Examples

			153 and 190 are members yielding 351 and 091. But 66, 666 are not members.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A069674, A095869, A095870.

Programs

Mathematica

trl=Rest[FoldList[Plus, 0, Range[2000]]]; okQ[n_] := Module[{p=Complement[FromDigits/@Permutations[IntegerDigits[n]], {n}]}, Length[Intersection[p, trl]]>0]; Select[Take[trl, 100], okQ]
Select[Accumulate[Range[150]],Count[FromDigits/@Permutations[IntegerDigits[#]],?(OddQ[ Sqrt[ 8#+1]]&)]>1&] (* _Harvey P. Dale, Nov 21 2023 *)

PARI

isok(t) = {my(d=digits(t)); forperm(#d, p, my(tt = fromdigits(Vec(vector(#d, k, d[p[k]])))); if ((tt!=t) && ispolygonal(tt, 3), return (1)); ); return(0); }
lista(nn) = {for (n=0, nn, my(t=n*(n+1)/2); if (isok(t), print1(t, ", ")); ); } \\ Michel Marcus, May 04 2021

Extensions

More terms from Harvey P. Dale, Nov 22 2002

Extended by Ray Chandler, Jun 29 2004

Offset changed to 1 by Jinyuan Wang, Aug 06 2021