%I #32 Jul 07 2022 19:52:27
%S 1,2,33,4554,57877875,7021243003421196,
%T 81446984612990832809030548964517,
%U 8388153908186958083116465238561550559414647202908596818094507838
%N a(1)=1. At any step consider the terms as two streams of digits: the first read from left to right and the second from right to left. Sum the two numbers and add them as new term of the sequence. Repeat.
%H Paolo P. Lava, <a href="/A269632/b269632.txt">Table of n, a(n) for n = 1..11</a>
%F Sum_{k >= 1} a(k)/a(k+1) = 0.567931128577306235186022447895934719336343085...
%F a(n) == 0 (mod 9), for n>3. - _Ivan N. Ianakiev_, Mar 08 2016
%e First step: 1; the two numbers are obviously 1 and 1 which sum to 2; sequence becomes 1, 2.
%e Second step: 1, 2; the two numbers are 12 and 21 that sum to 33; sequence becomes 1, 2, 33.
%e Third step: 1, 2, 33: the two numbers are 1233 and 3321 that sum to 4554; sequence becomes 1, 2, 33, 4554; etc.
%p P:=proc(q) local a,b,c,d,k,n; a:=[1]; print(1);
%p for n from 1 to q do b:=a[1]; for k from 2 to nops(a) do b:=10*b+a[k]; od;
%p c:=a[nops(a)]; for k from nops(a)-1 by -1 to 1 do c:=10*c+a[k]; od; d:=b+c; print(d);
%p for k from 1 to ilog10(d)+1 do a:=[op(a),(trunc(d/10^(ilog10(d)+1-k)) mod 10)]; od;
%p od; print(); end: P(15);
%t a = {1}; Do[AppendTo[a, FromDigits@ # + FromDigits@ Reverse@ # &@ Flatten@ Map[IntegerDigits, a]], {n, 2, 9}]; a (* _Michael De Vlieger_, Mar 03 2016 *)
%K nonn,base,easy
%O 1,2
%A _Paolo P. Lava_, Mar 02 2016