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

1,1

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A069674, A095869, A095870.

Sequence in context: A163309 A163165 A110957 * A117833 A117832 A268763

Adjacent sequences: A077668 A077669 A077670 * A077672 A077673 A077674

Keyword

nonn,base

Author

Amarnath Murthy, Nov 16 2002

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

Status

approved