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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). 3

%I

%S 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,

%T 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,

%U 4,4,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2

%N 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).

%H Felix Fröhlich, <a href="/A270172/b270172.txt">Table of n, a(n) for n = 0..10000</a>

%e 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.

%e 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.

%o (PARI) eva(n) = subst(Pol(n), x, 10)

%o increasedigits(n) = my(d=digits(n)); for(k=1, #d, d[k]++; if(d[k]==10, d[k]=0)); eva(d)

%o a(n) = my(x=n, i=0); while(#Str(x) > 1, x=increasedigits(x); i++); i

%Y Cf. A256079, A270173.

%K nonn,base

%O 0,11

%A _Felix Fröhlich_, Mar 12 2016

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Last modified October 18 13:47 EDT 2021. Contains 348068 sequences. (Running on oeis4.)