

A209674


For each n, define a sequence of numbers by S(0)=n, S(i) = sum of last two digits of the concatenation S(0)S(1)S(2)...S(i1); a(n) = smallest m such that S(m) = 5, or 1 if 5 is never reached.


2



1, 4, 9, 9, 5, 0, 4, 3, 10, 11, 5, 3, 2, 6, 1, 5, 8, 7, 9, 6, 10, 7, 8, 1, 7, 4, 3, 10, 6, 4, 10, 2, 1, 8, 5, 8, 7, 6, 4, 3, 6, 1, 4, 7, 4, 3, 6, 4, 3, 7, 1, 9, 11, 5, 8, 6, 4, 3, 7, 2, 5, 8, 7, 4, 6, 4, 3, 7, 2, 6, 4, 10, 5, 6, 4, 3, 7, 2, 6, 9, 11, 7, 6, 4, 3, 7, 2, 6, 9, 8, 12, 6, 4, 3, 7, 2, 6, 9, 8, 10
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OFFSET

0,2


COMMENTS

a(n) = 1 iff n ends in 00 (e.g. 100, 200, ...). (It is sufficient to check the 100 starts i,j, 0 <= i, j <= 9.)
5 is the unique number common to the trajectories of all numbers from 1 to 99.
Iterate the map k > A209685(k), starting at n, until reaching 5, or 1 if 5 is never reached.


REFERENCES

Eric Angelini, Posting to Math Fun Mailing List, Mar 11 2012.


LINKS

Table of n, a(n) for n=0..99.


FORMULA

The sequence is ultimately periodic.


EXAMPLE

For n=4 we have S(0)=4, S(1)=4, S(2)=8, S(3)=12, S(4)=3, S(5)=5, so a(4)=5.


PROG

(PARI) a(n)=my(m=0, t, k); while(n!=5, t=if(n>9, n%100\10+n%10, n+m%10); m=n; n=t; k++); k \\ Charles R Greathouse IV


CROSSREFS

Cf. A209685, A209686.
Sequence in context: A203140 A011512 A200642 * A157300 A100555 A250126
Adjacent sequences: A209671 A209672 A209673 * A209675 A209676 A209677


KEYWORD

sign,base


AUTHOR

N. J. A. Sloane, Mar 11 2012


EXTENSIONS

Corrected and extended by Charles R Greathouse IV, Mar 11 2012


STATUS

approved



