A269632 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.

1, 2, 33, 4554, 57877875, 7021243003421196, 81446984612990832809030548964517, 8388153908186958083116465238561550559414647202908596818094507838

Offset

1,2

Links

Paolo P. Lava, Table of n, a(n) for n = 1..11

Formula

Sum_{k >= 1} a(k)/a(k+1) = 0.567931128577306235186022447895934719336343085...

a(n) == 0 (mod 9), for n>3. - Ivan N. Ianakiev, Mar 08 2016

Example

First step: 1; the two numbers are obviously 1 and 1 which sum to 2; sequence becomes 1, 2.
Second step: 1, 2; the two numbers are 12 and 21 that sum to 33; sequence becomes 1, 2, 33.
Third step: 1, 2, 33: the two numbers are 1233 and 3321 that sum to 4554; sequence becomes 1, 2, 33, 4554; etc.

Maple

P:=proc(q) local a, b, c, d, k, n; a:=[1]; print(1);
for n from 1 to q do b:=a[1]; for k from 2 to nops(a) do b:=10*b+a[k]; od;
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);
for k from 1 to ilog10(d)+1 do a:=[op(a), (trunc(d/10^(ilog10(d)+1-k)) mod 10)]; od;
od; print(); end: P(15);

Mathematica

a = {1}; Do[AppendTo[a, FromDigits@ # + FromDigits@ Reverse@ # &@ Flatten@ Map[IntegerDigits, a]], {n, 2, 9}]; a (* Michael De Vlieger, Mar 03 2016 *)

Crossrefs

Sequence in context: A302452 A113105 A132567 * A083459 A368899 A034173

Adjacent sequences: A269629 A269630 A269631 * A269633 A269634 A269635

Keyword

nonn,base,easy

Author

Paolo P. Lava, Mar 02 2016

Status

approved