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A338379
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Floor of (digital root of n) divided by (number of digits in n).
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1
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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
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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Array[Floor[If[#1 == 0, 0, (#2 /. 0 -> 9)/IntegerLength[#1]]] & @@ {#, Mod[#, 9]} &, 105, 0] (* Michael De Vlieger, Nov 05 2020 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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