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A193585
Number of cycles under iteration of sum of squares of digits in base b.
5
0, 1, 0, 1, 1, 2, 3, 2, 1, 2, 4, 3, 2, 7, 1, 2, 1, 3, 1, 6, 2, 8, 4, 6, 1, 5, 4, 6, 2, 8, 6, 5, 3, 5, 4, 5, 3, 6, 1, 7, 6, 6, 2, 5, 4, 11, 4, 4, 4, 6, 3, 11, 4, 9, 4, 8, 4, 6, 6, 5, 4, 9, 6, 5, 2, 6, 3, 7, 7, 8, 5, 14, 5, 8, 3, 6, 3, 4, 5, 10, 5, 10, 6, 8, 5
OFFSET
2,6
COMMENTS
If b>=2 and a>=b^2 then S(a,2,b)<a. For each positive integer a, there is an positive integer m such that S^m(a,2,b)<b^2. (Grundman/Teeple, 2001, Lemma 6 and Corollary 7).
LINKS
H. G. Grundman, E. A. Teeple, Generalized Happy Numbers, Fibonacci Quarterly 39 (2001), nr. 5, p. 462-466.
EXAMPLE
In the decimal system all integers go to (1) or (4, 16, 37, 58, 89, 145, 42, 20) under the iteration of sum of squares of digits, hence there is one fixed point and one cycle. Therefore a(10) = 1.
CROSSREFS
Sequence in context: A114409 A340680 A343897 * A245436 A285581 A222173
KEYWORD
nonn,base
AUTHOR
Martin Renner, Jul 31 2011
STATUS
approved