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
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
Programs
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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