A309997 Number of paths from 2 to n of length A307092(n) - 1 via maps of the form x -> x + x^j, where j is a nonnegative integer.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2

Offset: 2

Author

Peter Kagey, Aug 26 2019

Keywords

• nonn

Comments

This sequence counts paths starting from 2 since there are an infinite number of maps from 1 to 2 via 1 -> 1 + 1^j.

Records occur at 2, 12, 226, 372, 744, 1490, 139511, ...

Examples

			For n = 520, the a(520) = 3 sequences of A307092(520)-1 = 3 maps are:
2 -> 2 + 2^1 -> 4 + 4^1     -> 8 + 8^3     = 520
2 -> 2 + 2^1 -> 4 + 4^4     -> 260 + 260^1 = 520
2 -> 2 + 2^7 -> 130 + 130^1 -> 260 + 260^1 = 520
With exponents (1,1,3), (1,4,1), and (7,1,1) respectively.
		

Links

• Peter Kagey, Table of n, a(n) for n = 2..10000
• Peter Kagey, Count the number of paths to n, Code Golf Stack Exchange.

Crossrefs

Cf. A307074, A307092.