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

Author

Felix Fröhlich, Mar 12 2016

Keywords

• nonn
• base

Examples

			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.
		

Links

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

Crossrefs

Cf. A256079, A270173.

Programs

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