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A343644
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a(n) is the sum of the number of occurrences of each digit of n up to and including that digit.
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1
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1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 7, 8, 9, 10, 11, 12, 13, 14, 5, 17, 11, 10, 11, 12, 13, 14, 15, 16, 7, 19, 20, 15, 13, 14, 15, 16, 17, 18, 9, 21, 22, 23, 19, 16, 17, 18, 19, 20, 11, 23, 24, 25, 26, 23, 19, 20, 21, 22, 13, 25, 26, 27, 28, 29, 27, 22, 23, 24, 15, 27
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listen;
history;
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OFFSET
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1,10
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LINKS
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EXAMPLE
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a(10) = 3 as the digit 1 is the second digit 1 and the digit 0 is the first digit 0 giving 2+1.
a(22) is 11 as the digits of 22 are 2 and 2. Before 22 the digit 2 occurred four times, in 2, 12, 20 in 21. The first 2 in 22 is the fifth in total. The second 2 in 22 is the sixth 2 in total giving 5 + 6.
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MATHEMATICA
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Array[Sum[Count[Flatten@Join[IntegerDigits/@Range[#-1], a[[;; k]]], a[[k]]], {k, Length[a=IntegerDigits@#]}]&, 100] (* Giorgos Kalogeropoulos, Apr 23 2021 *)
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PROG
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(PARI) first(n) = my(v=vector(10), res=vector(n)); for(i=1, n, c=0; d=digits(i); for(i=1, #d, v[d[i]+1]++; c+=v[d[i]+1]); res[i]=c); res
(Python)
def aupto(limit):
f, alst = [0 for i in range(10)], []
for n in range(1, limit+1):
s = 0
for d in list(map(int, str(n))): f[d] += 1; s += f[d]
alst.append(s)
return alst
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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