A055640 Number of nonzero digits in decimal expansion of n.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2

Offset: 0

Author

Henry Bottomley, Jun 06 2000

Keywords

• nonn
• base
• easy
• nice

Comments

Comment from Antti Karttunen, Sep 05 2004: (Start)

Also number of characters needed to write the number n in classical Greek alphabetic system, up to n=999. The Greek alphabetic system assigned values to the letters as follows:

alpha = 1, beta = 2, gamma = 3, delta = 4, epsilon = 5, digamma = 6, zeta = 7, eta = 8, theta = 9, iota = 10, kappa = 20, lambda = 30, mu = 40, nu = 50, xi = 60, omicron = 70, pi = 80, koppa = 90, rho = 100, sigma = 200, tau = 300, upsilon = 400, phi = 500, chi = 600, psi = 700, omega = 800, sampi = 900. (End)

For partial sums see A102685. - Hieronymus Fischer, Jun 06 2012

Examples

			129 is written as rho kappa theta in the old Greek system.
		

References

• L. Threatte, The Greek Alphabet, in The World's Writing Systems, edited by Peter T. Daniels and William Bright, Oxford Univ. Press, 1996, p. 278.

Links

• Hieronymus Fischer, Table of n, a(n) for n = 0..10000
• Unicode Consortium, Unicode Home Page. (Follow the link "Display Problems?" to find an appropriate information/font file to show the Greek characters correctly. Or look at the HTML source to see their names.)

Crossrefs

Cf. A102669-A102685, A004719, A011540, A052382, A061745, A054899, A055641, A055642, A122840, A160093, A160094, A193238, A196563, A195564, A000120, A000788, A023416, A059015 (for base 2).

Differs from A098378 for the first time at position n=200 with a(200)=1, as only one nonzero Arabic digit (and only one Greek letter) is needed for two hundred, while A098378(200)=2 as two characters are needed in the Ethiopic system.

Programs

Haskell

a055640 n = length $ filter (/= '0') $ show n
-- Reinhard Zumkeller, May 02 2011

Mathematica

Table[Count[IntegerDigits[n],?(#>0&)],{n,0,120}] (* _Harvey P. Dale, Mar 11 2012 *)
Total[Most[DigitCount[#]]]&/@Range[0,120] (* Harvey P. Dale, Mar 19 2021 *)

PARI

a(n)=my(v=digits(n));sum(i=1,#v,!!v[i]) \\ Charles R Greathouse IV, Aug 05 2012

Formula

From Hieronymus Fischer, Jun 06 2012: (Start)

a(n) = Sum_{j=1..m+1} (floor(n/10^j+0.9) - floor(n/10^j)), where m = floor(log_10(n)).

a(n) = m + 1 - A055641(n).

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

a(n) = A055642(n) - A055641(n).