[seqfan] Re: a(a(n)) is a triangular number

[Eric Angelini]

Hello SeqFans,
< Aai > has computed the first 100 terms of T. Here is
part of his message.
Best,
É.

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[Eric]:
... and to build T: always use the smallest integer not
    yet present in T and not leading to a contradiction :

T = 1,3,6,2,7,10,15,9,21,28,12,36,14,45,55,17,66,19,78,22,91,105,24,...
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[Aai]:
> (...) Just for the record: this method produces one
  million elements in less then 1.7 seconds (32bit 3 Ghz PC).

So here are the first 100:
( T17 is the J-generator )

    10 10 $ T17 100

    1    3    6    2    7   10   15    9   21   28
   12   36   14   45   55   17   66   19   78   22
   91  105   24  120   26  136   29  153  171   31
  190   33  210   35  231  253   38  276   40  300
   42  325   44  351  378   47  406   49  435   51
  465   53  496   56  528  561   58  595   60  630
   62  666   64  703   67  741  780   69  820   71
  861   73  903   75  946   77  990 1035   80 1081
   82 1128   84 1176   86 1225   88 1275   90 1326
1378   93 1431   95 1485   97 1540   99 1596  101

A proof (with J) that all a(a(i) are triangular numbers:

    *./ isDhg R{~(#~N>])<: R=.T17 N=.100
1

isDhg tests n for being a triangular number (1 = true)

Met vriendelijke groet,
=@@i
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