A209686 For each n, define a sequence of numbers by S(0)=n, S(i) = sum of last three digits of the concatenation S(0)S(1)S(2)...S(i-1); a(n) = smallest m such that S(m) = 11, or -1 if 11 is never reached.

-1, 6, 8, 14, 7, 6, 13, 16, 6, 7, 5, 0, 3, 8, 6, 13, 16, 6, 7, 7, 15, 11, 7, 6, 13, 16, 6, 7, 9, 1, 9, 15, 6, 13, 16, 6, 7, 12, 1, 10, 4, 6, 13, 16, 6, 7, 9, 1, 2, 4, 6, 13, 16, 6, 7, 5, 1, 20, 13, -1, 13, 16, 6, 7, 4, 1, 12, 2, 5, 3, 16, 6, 7, 10, 1, 3, 11, 15, 6, 13, 6, 7, 19, 1, 14, 6, 2, 7, 5, 9, 7, 9, 1, 12, 4, 5

Offset

0,2

References

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

Links

Table of n, a(n) for n=0..95.

Example

3->3->6->12->9->12->12->5->8->15->14->10->5->6->11, so a(3)=14.
59->14->14->9->14->14->9->... never reaches 11, so a(59)=-1.

Crossrefs

Cf. A209674.

Sequence in context: A315877 A315878 A101729 * A283286 A283375 A242758

Adjacent sequences: A209683 A209684 A209685 * A209687 A209688 A209689

Keyword

sign,base

Author

N. J. A. Sloane, Mar 11 2012

Status

approved