A045777 a(1)=1, a(2)=2; thereafter successive products of pairs of digits make further digits.

1, 2, 2, 4, 8, 3, 2, 2, 4, 6, 4, 8, 2, 4, 2, 4, 3, 2, 1, 6, 8, 8, 8, 1, 2, 6, 2, 6, 4, 8, 6, 4, 6, 4, 8, 2, 1, 2, 1, 2, 1, 2, 2, 4, 3, 2, 4, 8, 2, 4, 2, 4, 2, 4, 3, 2, 1, 6, 2, 2, 2, 2, 2, 2, 4, 8, 1, 2, 6, 8, 3, 2, 1, 6, 8, 8, 8, 8, 8, 1, 2, 6, 2, 6, 1, 2, 4, 4, 4, 4, 4, 8, 3, 2, 8, 2, 1, 2, 4, 8, 2, 4, 6, 2, 6

Offset

1,2

Comments

The numbers 0, 5, 7, and 9 never appear, but arbitrarily long sequences of 8's appear.

Links

T. D. Noe, Table of n, a(n) for n = 1..15212

Erich Friedman, Puzzles of the Week.

Example

1*2=2 2*2=4 2*4=8 4*8=32 8*3=24...

Mathematica

t = {1, 2}; Do[ t = Join[t, IntegerDigits[t[[n-1]] t[[n-2]]]], {n, 3, 100}]; t

Prog

(Python)
from itertools import islice
from collections import deque
def agen(): # generator of terms
    a = deque([1, 2])
    while True:
        a.extend(list(map(int, str(a[0]*a[1]))))
        yield a.popleft()
print(list(islice(agen(), 105))) # Michael S. Branicky, Feb 15 2024

Crossrefs

Sequence in context: A112059 A394055 A093094 * A136534 A121175 A368515

Adjacent sequences: A045774 A045775 A045776 * A045778 A045779 A045780

Keyword

easy,nonn,base

Author

Erich Friedman

Status

approved