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A102680 Number of digits >= 7 in the decimal representations of all integers from 0 to n. 2
0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 32, 34, 35, 36 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

The total number of digits >= 7 occurring in all the numbers 0, 1, 2, ... n (in decimal representation). - Hieronymus Fischer, Jun 10 2012

LINKS

Hieronymus Fischer, Table of n, a(n) for n = 0..10000

FORMULA

Contribution from Hieronymus Fischer, Jun 10 2012: (Start)

a(n) = (1/2)*sum_{j=1..m+1} (floor(n/10^j + 7/10)*(2n + 2 - (2/5 + floor(n/10^j + 7/10))*10^j) - floor(n/10^j)*(2n + 2 - (1+floor(n/10^j)) * 10^j)), where m=floor(log_10(n)).

a(n) = (n+1)*A102679(n) + (1/2)*sum_{j=1..m+1} (((-2/5)*floor(n/10^j + 7/10) + floor(n/10^j))*10^j - (floor(n/10^j + 7/10)^2 - floor(n/10^j)^2)*10^j), where m=floor(log_10(n)).

a(10^m-1) = 3*m*10^(m-1).

(this is total number of digits >= 7 occurring in all the numbers with <= m places).

G.f.: g(x) = (1/(1-x)^2)*sum_{j>=0} (x^(7*10^j) - x^(10*10^j))/(1-x^10^(j+1)). (End)

MAPLE

p:=proc(n) local b, ct, j: b:=convert(n, base, 10): ct:=0: for j from 1 to nops(b) do if b[j]>=7 then ct:=ct+1 else ct:=ct fi od: ct: end:

seq(add(p(i), i=0..n), n=0..90);

# Emeric Deutsch

MATHEMATICA

Accumulate[Table[Count[IntegerDigits[n], _?(#>6&)], {n, 0, 90}]] (* Harvey P. Dale, Sep 04 2018 *)

CROSSREFS

Partial sums of A102679.

Cf. A027868, A054899, A055640, A055641, A102669-A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564. Partial sums of A102669.

Cf. A000120, A000788, A023416, A059015 (for base 2).

Sequence in context: A185436 A025794 A025793 * A025791 A237115 A069637

Adjacent sequences:  A102677 A102678 A102679 * A102681 A102682 A102683

KEYWORD

nonn,base,easy

AUTHOR

N. J. A. Sloane, Feb 03 2005

EXTENSIONS

More terms from Emeric Deutsch, Feb 23 2005

STATUS

approved

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Last modified November 17 08:17 EST 2018. Contains 317275 sequences. (Running on oeis4.)