A270173 -id:A270173 - cp's OEIS frontend

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

Felix Fröhlich, Mar 12 2016

			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.

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

Cf. A256079, A270173.

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

A269667 a(n) = A270172(10*n).

Original entry on oeis.org

0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 13, 12, 11, 10, 9, 8, 7

Offset: 0

Felix Fröhlich, Mar 13 2016

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

Cf. A270172, A270173.

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)
a270172(n) = my(x=n, i=0); while(#Str(x) > 1, x=increasedigits(x); i++); i
a(n) = a270172(10*n)

cp's OEIS Frontend

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).

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