OFFSET
1,2
COMMENTS
A more formal definition can be given as follows: a(1) = 1; for n > 1, let x be the least significant digit of a(n-1); then a(n) = a(n-1) * (10*x + y), with y being the most significant digit of a(n). Choose the smallest such y if such a y exists. If no such y exists, the sequence ends. We also restrict y to being a nonzero digit.
The sequence is given in its entirety as there is no possible next term after 5846151300.
Choosing other values for a(1) yields finite sequences up to a(1) = 10000 as long as a(1) is not of the form 1...0 otherwise the sequence is constant and infinite. For example, if a(1) = 120, then a(2) = 120 because 120 * 01 = 120.
EXAMPLE
Replace each comma in the original sequence by the pair of digits adjacent to the comma; the result is the sequence of first ratios between the terms of the sequence:
Sequence: 1, 11, 121, 1331, 14641, 161051, 1771561, 19487171, 233846052, 5846151300
Ratios: 11, 11, 11, 11, 11, 11, 11, 12, 25
For example: a(9) = 233846052 = 12 * 19487171 = 12 * a(8)
MATHEMATICA
a[1] = 1; a[n_] := a[n] = For[x = Mod[a[n - 1], 10]; y = 1, y <= 9, y++, an = a[n - 1]*(10*x + y); If[y == IntegerDigits[an][[1]], Return[an]]]; Array[a, 10]
CROSSREFS
KEYWORD
nonn,base,fini,full
AUTHOR
Nicholas M. R. Frieler, Jul 17 2024
STATUS
approved