A160862 - OEIS

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

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C. Suriano, Miniature Matematiche, unpublished, 2009, section 30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