A270172 Number of steps required to reach a single-digit number when successively increasing all digits of n by 1 simultaneously and removing leading zeros (9 becomes 0).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2

Offset

0,11

Links

Felix Fröhlich, Table of n, a(n) for n = 0..10000

Example

For n = 11: Successively increasing the digits of n yields the sequence s(t) (starting with t = 0): 11, 22, 33, 44, 55, 66, 77, 88, 99, 0. s(9) = 0, so a(11) = 9.
For n = 15: The sequence s(t) (again starting with t = 0): 15, 26, 37, 48, 59, 60, 71, 82, 93, 4. s(9) = 4, so a(15) = 9.

Prog

(PARI) eva(n) = subst(Pol(n), x, 10)
increasedigits(n) = my(d=digits(n)); for(k=1, #d, d[k]++; if(d[k]==10, d[k]=0)); eva(d)
a(n) = my(x=n, i=0); while(#Str(x) > 1, x=increasedigits(x); i++); i

Crossrefs

Cf. A256079, A270173.

Sequence in context: A363117 A116667 A259151 * A332550 A137577 A363118

Adjacent sequences: A270169 A270170 A270171 * A270173 A270174 A270175

Keyword

nonn,base

Author

Felix Fröhlich, Mar 12 2016

Status

approved