A160862 a(n) = length of period of transformation sum-digit-square: given a number m(k) define m(k+1) to be the sum of the squares of the decimal digits of m(k) and iterate until m(s) is found such that m(s)=m(k) with k<s. Numbers repeat periodically with a period of length a(n).

1, 8, 12, 8, 11, 16, 5, 12, 11, 1, 9, 12, 2, 13, 10, 8, 12, 12, 4, 8, 11, 13, 3, 8, 10, 12, 13, 3, 9, 13, 2, 3, 12, 11, 12, 15, 8, 9, 13, 8, 13, 8, 11, 4, 14, 11, 11, 13, 4, 11, 10, 10, 12, 14, 12

Offset

1,2

References

C. Suriano, Miniature Matematiche, unpublished, 2009, section 30

Links

Table of n, a(n) for n=1..55.

Example

a(1)=1 since 1^2=1; a(2)=8 since the period contains 8 numbers: 4,16,37,58,89,145,42,20 the following being 4 again.
a(5)=11 since the sequence runs as follows:
25,29, 85, 89, 145, 42, 20, 4, 16, 37, 58 the next term being 89 that is already there.

Crossrefs

Cf. A152077.

Sequence in context: A220665 A166173 A014453 * A152077 A215696 A325809

Adjacent sequences: A160859 A160860 A160861 * A160863 A160864 A160865

Keyword

nonn,base

Author

Carmine Suriano, May 29 2009

Status

approved