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A277635
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Number of 7's appearing in the sequence of consecutive natural numbers from 1 to A007908(n), where A007908 = (1, 12, 123, 1234, ...).
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11
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OFFSET
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1,3
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COMMENTS
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First 6 terms are the same as in A083449, also see A272525. [See the OEIS wiki page for more details. - M. F. Hasler, Dec 29 2020]
a(n) gives the number of times the digit 7 occurs in all terms of A000027 in the interval [A000027(1), A007908(n)]. - Felix Fröhlich, Oct 28 2016
The sequence was initially defined only up to n = 9 and then extended using A007908 = concat(1..n); see A277837 for the extension using A014824 (a(n) = 10 a(n-1) + n) leading to a smoother growth, in particular at powers of 10. - M. F. Hasler, Nov 01 2016, edited Dec 29 2020
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LINKS
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Table of n, a(n) for n=1..9.
Puzzling Stack Exchange, How many sevens?
M. F. Hasler, Digits d in 0 through 123...n, OEIS Wiki, Nov. 2016.
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EXAMPLE
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22 is the third term of the sequence because there are 22 occurrences of the digit '7' contained in numbers within the range of 1 to 123.
96022049 is the 9th term of the sequence because there are 96022049 occurrences of the digit '7' contained in numbers within the range of 1 to 123456789.
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MATHEMATICA
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Table[a[n] = Count[Flatten@ Map[IntegerDigits, Range@ FromDigits@ Range@ n], k_ /; k == 8]; Print@ a@ n; an = a[n]; an, {n, 0, 9}] (* Michael De Vlieger, Oct 30 2016 *)
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PROG
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(PARI) print1(c=0); N=1; for(n=2, 8, print1(", "c+=sum(k=N+1, N=eval(Str(N, n)), #select(d->d==7, digits(k))))) \\ For illustration; more efficient code below. - M. F. Hasler, Oct 31 2016
(PARI) A277635(n, m=7)=if(n>m, A277635(n, m+1)+(m+2)*10^(n-m-1), A277830(n)-(m>n)) \\ Valid only for n <= 9. - M. F. Hasler, Nov 02 2016
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CROSSREFS
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Cf. A083449, A272525, A014824.
Cf. A277830 - A277838 and A277849: analog for digits 0 .. 9, but based on A014824 instead of A083449.
Sequence in context: A272525 A277849 A277838 * A277837 A277836 A277835
Adjacent sequences: A277632 A277633 A277634 * A277636 A277637 A277638
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KEYWORD
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nonn,base
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AUTHOR
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Alexander R. Povolotsky, Oct 24 2016
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STATUS
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approved
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