OFFSET
1,2
COMMENTS
If we want the sequence to be the lexicographically earliest permutation of the integers > 0, we must start with a(1) = 1 and a(2) = 11. With a(2) < 11, the sequence stops immediately.
LINKS
Eric Angelini, Cumulative Sums, Personal blog.
EXAMPLE
a(1) = 1
a(1) * a(2) = 11
a(1) * a(2) * a(3) = 22
a(1) * a(2) * a(3) * a(4) = 550
a(1) * a(2) * a(3) * a(4) * a(5) = 27500
a(1) * a(2) * a(3) * a(4) * a(5) * a(6) = 742500; etc.
The succession of the above results is:
1, 11, 22, 550, 27500, 742500, ...
The first terms of the sequence are:
1, 11, 2, 25, 50, 27, 500, 7, 4, 2500,, ...
We see that the successive digits are the same in the two sequences.
MATHEMATICA
Nest[(a=#; AppendTo[a, (new=Flatten[IntegerDigits/@Table[Times@@a[[;; i]], {i, Length@a}]][[Length@Flatten[IntegerDigits/@a]+1;; ]];
k=1; While[MemberQ[a, FromDigits@new[[;; k]]]||new[[k+1]]==0, k++]; FromDigits@new[[;; k]])])&, {1, 11, 2, 25}, 45] (* Giorgos Kalogeropoulos, Aug 05 2023 *)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eric Angelini, Aug 03 2023
STATUS
approved