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%I #20 Nov 21 2023 12:48:08
%S 10,105,120,153,190,210,253,300,325,351,496,630,780,820,946,1035,1378,
%T 1485,1830,1891,2080,2145,2415,2701,2850,3081,3160,3570,3655,3741,
%U 3916,4005,4095,4371,4560,4851,4950,5050,5356,5460,5565,5778,6105,6555,7021
%N Triangular numbers whose digit permutations yield at least one further triangular number.
%H Harvey P. Dale, <a href="/A077671/b077671.txt">Table of n, a(n) for n = 1..2000</a>
%e 153 and 190 are members yielding 351 and 091. But 66, 666 are not members.
%t 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]
%t Select[Accumulate[Range[150]],Count[FromDigits/@Permutations[IntegerDigits[#]],_?(OddQ[ Sqrt[ 8#+1]]&)]>1&] (* _Harvey P. Dale_, Nov 21 2023 *)
%o (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); }
%o lista(nn) = {for (n=0, nn, my(t=n*(n+1)/2); if (isok(t), print1(t, ", ")); ); } \\ _Michel Marcus_, May 04 2021
%Y Cf. A069674, A095869, A095870.
%K nonn,base
%O 1,1
%A _Amarnath Murthy_, Nov 16 2002
%E More terms from _Harvey P. Dale_, Nov 22 2002
%E Extended by _Ray Chandler_, Jun 29 2004
%E Offset changed to 1 by _Jinyuan Wang_, Aug 06 2021
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