A338379 Floor of (digital root of n) divided by (number of digits in n).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 1, 2, 2, 3, 3, 4, 4, 0, 1, 1, 2, 2, 3, 3, 4, 4, 0, 1, 1, 2, 2, 3, 3, 4, 4, 0, 1, 1, 2, 2, 3, 3, 4, 4, 0, 1, 1, 2, 2, 3, 3, 4, 4, 0, 1, 1, 2, 2, 3, 3, 4, 4, 0, 1, 1, 2, 2, 3, 3, 4, 4, 0, 1, 1, 2, 2, 3, 3, 4, 4, 0, 1, 1, 2, 2

Offset

0,3

Links

Fernando Villanueva, Table of n, a(n) for n = 0..9999

Example

For n = 12345 the length of n is 5 (because 12345 has 5 digits) and its digital root is 6 (1+2+3+4+5=15 then 1+5=6). Then [6/5]=1 (where [x] is the integer part of x). Therefore a(12345)=0.

Mathematica

Array[Floor[If[#1 == 0, 0, (#2 /. 0 -> 9)/IntegerLength[#1]]] & @@ {#, Mod[#, 9]} &, 105, 0] (* Michael De Vlieger, Nov 05 2020 *)

Prog

(Python)
#Defines digital root
def recsum(n):
    nstr = str(n)
    if len(nstr) == 1:
        return int(nstr)
    else:
        nl = sum([int(j) for j in nstr])
        return recsum(nl)
#Prints first 1000 terms
for i in range(1000):
    print(recsum(i)//len(str(i)))
(PARI) a(n) = if (n, (n-1)%9+1, 0) \ #Str(n); \\ Michel Marcus, Nov 05 2020

Crossrefs

Cf. A010888 (digital root of n), A055642 (length of n).

Sequence in context: A031298 A004428 A004429 * A004426 A262188 A358647

Adjacent sequences: A338376 A338377 A338378 * A338380 A338381 A338382

Keyword

nonn,base

Author

Fernando Villanueva, Oct 23 2020

Status

approved