Almost fibonacci sequence
1235813941213533488671216141383377554111161
The rule for this sequence of digits is as follows:
Begin with digits 1 and 2. Add them together and append them to the end: 123
Take the second and third digits, add them together and append again: 1235
Continue to the third and fourth: 12358, then the fifth and sixth 1235813
We are adding digits, though not numbers so the next sum is 8+1 not 8+13: 12348139.
Question: What is the greatest number of 1's to appear in a row if this sequence is continued indefinitely.
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1 solution
The first instance of six 1's in a row begins at position 12,463 but we get a dying pattern:
111111 22222 4444 888 1616 777 1414 555 1010 111
However, a series of seven or more 1's would get a growing pattern which would lead to an infinite number of 1's in a row
1111111 222222 44444 8888 161616 77777 14141414 5555555 101010101010 11111111111
and indeed a sequence of nine 1's appears beginning at position 20,560
So there is no upper limit to the number of 1's.