A377086 Number of fixed points under iteration of the map sending a positive integer to the product of its leading base-n digit and the sum of the squares of its base-n digits.

1, 2, 2, 1, 1, 4, 3, 4, 2, 3, 1, 3, 5, 2, 4, 4, 2, 4, 1, 3, 3, 3, 1, 5, 2, 3, 5, 4, 4, 9, 2, 1, 1, 4, 2, 6, 4, 1, 2, 5, 3, 6, 3, 1, 2, 3, 1, 7, 2, 1, 3, 3, 1, 5, 4, 6, 5, 4, 2, 8, 3, 2, 7, 3, 1, 4, 4, 2, 3, 6, 3, 9, 2, 3, 4, 9, 3, 7, 3, 2, 6, 5, 1, 7, 3, 3, 3

Offset: 2

Author

N. Bradley Fox, Nathan Fox, Helen Grundman, Rachel Lynn, Changningphaabi Namoijam, Mary Vanderschoot, Oct 15 2024

Keywords

• nonn
• base

Comments

If b>=2 and a>=b^3 then E(a,2,b)

Unlike the related sequence A193583, which contains only odd numbers, this sequence contains even numbers and odd numbers.

Examples

			In the decimal system all integers go to (1), (298), (46, 208, 136), (26, 80, 512, 150), or (33, 54, 205, 58, 445, 228, 144) under iteration of the map A376270, hence there are two fixed points and three cycles. Therefore a(10) = 2.
		

Links

• Nathan Fox, Table of n, a(n) for n = 2..100
• N. Bradley Fox et al., Elated Numbers, arXiv:2409.09863 [math.NT], 2024.

Crossrefs

Cf. A376270, A376272, A377087, A377088.

A193583 is the analog for happy numbers.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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