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 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(i-1); 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified July 23 03:25 EDT 2019. Contains 325230 sequences. (Running on oeis4.)