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