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A243238 Table T(n,r) of terms in the reverse and add sequences of positive integers n read by antidiagonals.

%I A243238 #50 Oct 28 2021 06:29:44
%S A243238 1,2,2,4,4,3,8,8,6,4,16,16,12,8,5,77,77,33,16,10,6,154,154,66,77,11,
%T A243238 12,7,605,605,132,154,22,33,14,8,1111,1111,363,605,44,66,55,16,9,2222,
%U A243238 2222,726,1111,88,132,110,77,18,10,4444,4444,1353,2222,176,363,121,154,99,11,11
%N A243238 Table T(n,r) of terms in the reverse and add sequences of positive integers n read by antidiagonals.
%H A243238 Alois P. Heinz, <a href="/A243238/b243238.txt">Antidiagonals n = 1..141, flattened</a>
%H A243238 <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>
%e A243238 T(5,6) = 88, since 88 is the 6th term in the reverse and add sequence of 5.
%e A243238 Table starts with:
%e A243238   1 2 4 8 16 77 154 605 1111 2222
%e A243238   2 4 8 16 77 154 605 1111 2222 4444
%e A243238   3 6 12 33 66 132 363 726 1353 4884
%e A243238   4 8 16 77 154 605 1111 2222 4444 8888
%e A243238   5 10 11 22 44 88 176 847 1595 7546
%e A243238   6 12 33 66 132 363 726 1353 4884 9768
%e A243238   7 14 55 110 121 242 484 968 1837 9218
%e A243238   8 16 77 154 605 1111 2222 4444 8888 17776
%e A243238   9 18 99 198 1089 10890 20691 40293 79497 158994
%e A243238   10 11 22 44 88 176 847 1595 7546 14003
%p A243238 T:= proc(n, r) option remember; `if`(r=1, n, (h-> h +(s->
%p A243238       parse(cat(s[-i]$i=1..length(s))))(""||h))(T(n, r-1)))
%p A243238     end:
%p A243238 seq(seq(T(n, 1+d-n), n=1..d), d=1..12);  # _Alois P. Heinz_, Jun 18 2014
%t A243238 rad[n_] := n + FromDigits[Reverse[IntegerDigits[n]]];
%t A243238 T[n_, 1] := n; T[n_, k_] := T[n, k] = rad[T[n, k-1]];
%t A243238 Table[T[n-k+1, k], {n, 1, 12}, {k, n, 1, -1}] // Flatten (* _Jean-François Alcover_, Apr 08 2016 *)
%Y A243238 Rows n=1, 3, 5, 7, 9 give: A001127, A033648, A033649, A033650, A033651.
%Y A243238 Cf. A006960, A023108, A033670, A088753, A089694, A240510.
%Y A243238 Main diagonal gives A244058.
%K A243238 nonn,base,tabl
%O A243238 1,2
%A A243238 _Felix Fröhlich_, Jun 12 2014