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A364697
Lexicographically earliest permutation of the positive integers such that the successive cumulative products reproduce the sequence itself, digit by digit.
0
1, 11, 2, 25, 50, 27, 500, 7, 4, 2500, 3, 71, 250000, 259, 8, 750000, 10, 39, 5000000, 2598, 7500000000, 77, 9, 6, 2500000000, 5, 53, 533, 75000000001, 38, 383, 43, 75000000000000, 35, 84, 13, 103, 12, 5000000000000, 28, 67, 30, 48, 25000000000000000, 21, 504, 78, 61, 87
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
Sequence in context: A336904 A051309 A077344 * A298439 A095157 A110767
KEYWORD
base,nonn
AUTHOR
Eric Angelini, Aug 03 2023
STATUS
approved