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A208059 Start with n, successively subtract each digit of the resulting sequence (the digits of a negative term being the negatives of that term's digits): a(n) is the number of steps needed to get to the first zero. 16
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 48, 14, 76793, 385, 12, 232, 98, 24, 4, 6, 10952, 8, 575702095, 18, 82, 39, 16, 7, 6, 26, 9, 8, 30, 12, 13, 182, 449, 25, 62 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

COMMENTS

This is the same procedure used in A207505 with an allowance made to continue the process if we miss zero and enter negative territory on our initial downward run. A downward run will succumb to an upward run, and vice versa, with each run presenting another opportunity to hit zero. (A random-digit trail entails, per run, a 1 in 5 chance of hitting zero.)

a(23) was first computed by Nicolas Berr. According to his calculations, a(40) does not hit zero in its first 15 sign-change crossings. The 16th crossing is ~2*10^15.

If a negative number appears in column a, say -107, then in column b we write successively -1, 0, -7.

As far as I know, it is only a conjecture that for any starting value n we always reach a 0. - N. J. A. Sloane, Jun 01 2012

a(40) (at least 10^15) is the smallest unknown value.

LINKS

Table of n, a(n) for n=0..39.

Eric Angelini, Miss Numbers, Feb 2012

E. Angelini, Miss Numbers [Cached copy, with permission]

Christopher Creutzig, A208059 analogues (bases 2-16)

Christopher Creutzig, A208059 analogues (bases 2-16) [Cached copy made Jun 01 2012]

Hans Havermann, A208059 evolutions

EXAMPLE

When successively subtracting its own digit-trail, 12 requires 14 steps to hit its first zero, achieved on its first upward run, thus making a(12) = 14:

.a.....b......c

12  -  1  =  11

11  -  2  =   9

9   -  1  =   8

8   -  1  =   7

7   -  9  =  -2

-2  -  8  = -10

-10 -  7  = -17

-17 -(-2) = -15

-15 -(-1) = -14

-14 -(-0) = -14

-14 -(-1) = -13

-13 -(-7) =  -6

-6  -(-1) =  -5

-5  -(-5) =   0

etc., ad infinitum.

We get column b by reading column a digit-by-digit.

PROG

(PARI) A208059(n, v=0/*verbose: print all terms if >0*/, a=[])={ v&print1(n); a=eval(Vec(Str(n))); for(c=0, 9e9, n|return(c); a=concat(vecextract(a, "^1"), eval(Vec(Str(abs(n-=a[1]))))*sign(n)); v&print1(", "n)) }  \\- M. F. Hasler, Mar 03 2012

CROSSREFS

Cf. A207505, A207506.

Sequence in context: A088718 A219162 A016548 * A162333 A003878 A219056

Adjacent sequences:  A208056 A208057 A208058 * A208060 A208061 A208062

KEYWORD

nonn,base,more

AUTHOR

Hans Havermann, Feb 23 2012

EXTENSIONS

More terms from Hans Havermann, Mar 06 2012

Edited by N. J. A. Sloane, Jun 01 2012

STATUS

approved

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Last modified March 23 04:40 EDT 2017. Contains 283905 sequences.