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A014261 Numbers that contain odd digits only. 36
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 31, 33, 35, 37, 39, 51, 53, 55, 57, 59, 71, 73, 75, 77, 79, 91, 93, 95, 97, 99, 111, 113, 115, 117, 119, 131, 133, 135, 137, 139, 151, 153, 155, 157, 159, 171, 173, 175, 177, 179, 191, 193, 195, 197, 199, 311, 313, 315, 317, 319 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Or, numbers whose product of digits is odd.

A121759(a(n)) = a(n); A000035(A007959(a(n))) = 1. - Reinhard Zumkeller, Nov 30 2007

a(n+1) - a(n) = A164898(n). - Reinhard Zumkeller, Aug 30 2009

Complement of A007928; A196563(a(n)) = 0. - Reinhard Zumkeller, Oct 04 2011

If n is represented as a zerofree base-5 number (see A084545) according to n = d(m)d(m-1)...d(3)d(2)d(1)d(0) then a(n) = sum_{j = 0..m} c(d(j))*10^j, where c(k) = 1, 3, 5, 7, 9 for k = 1..5. - Hieronymus Fischer, Jun 06 2012

a(n) = A225985(A226091(n)).- Reinhard Zumkeller, May 26 2013

LINKS

R. Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for 10-automatic sequences.

FORMULA

From Reinhard Zumkeller, Aug 30 2009: (Start)

a(n+1) = h(a(n)) with h(x) = 1 + (if x mod 10 < 9 then x + x mod 2 else 10*h(floor(x/10)));

a(n) = f(n, 1) where f(n, x) = if n = 1 then x else f(n-1, h(x)). (End)

From Hieronymus Fischer, Jun 06 2012: (Start)

a(n) = sum_{j = 0..m-1} ((2*b_j(n)+1) mod 10)*10^j, where b_j(n)) = floor((4*n+1-5^m)/(4*5^j)), m = floor(log_5(4*n+1)).

a(1*(5^n-1)/4) = 1*(10^n-1)/9.

a(2*(5^n-1)/4) = 1*(10^n-1)/3.

a(3*(5^n-1)/4) = 5*(10^n-1)/9.

a(4*(5^n-1)/4) = 7*(10^n-1)/9.

a(5*(5^n-1)/4) = 10^n - 1.

a((5^n-1)/4 + 5^(n-1)-1) = (10^n-5)/5.

a(n) = (10^log_5(4*n+1)-1)/9 for n = (5^k-1)/4, k > 0.

a(n) < (10^log_5(4*n+1)-1)/9 for (5^k-1)/4 < n < (5^(k+1)-1)/4, k > 0.

a(n) <= 27/(9*2^log_5(9)-1)*(10^log_5(4*n+1)-1)/9 for n > 0, equality holds for n = 2.

a(n) > 0.776*10^log_5(4*n+1)-1)/9 for n > 0.

a(n) >= A001742(n), equality holds for n = (5^k-1)/4, k > 0.

a(n) = A084545(n) if and only if all digits of A084545(n) are 1, else a(n) > A084545(n).

G.f.: g(x)= (x^(1/4)*(1-x))^(-1) sum_{j = 0..infinity} 10^j*z(j)^(5/4)*(1-z(j))*(1 + 3*z(j) + 5*z(j)^2 + 7*z(j)^3 + 9*z(j)^4)/(1-z(j)^5), where z(j) = x^5^j.

Also: g(x) = (1/(1-x))*(h_(5,0)(x) + 2*h_(5,1)(x) + 2*h_(5,2)(x) + 2*h_(5,3)(x) + 2*h_(5,4)(x) - 9*h_(5,5)(x)), where h_(5,k)(x) = sum_{j >= 0} 10^j*x^((5^(j+1)-1)/4)*(x^5^j)^k/(1-(x^5^j)^5). (End)

EXAMPLE

a(10^3) = 13779.

a(10^4) = 397779.

a(10^5) = 11177779.

a(10^6) = 335777779.

MATHEMATICA

Select[Range[400], OddQ[Times@@IntegerDigits[#]] &] (* Alonso del Arte, Feb 21 2014 *)

PROG

(MAGMA) [ n : n in [1..129] | IsOdd(&*Intseq(n, 10)) ];

(Haskell)

a014261 n = a014261_list !! (n-1)

a014261_list = filter (all (`elem` "13579") . show) [1, 3..]

-- Reinhard Zumkeller, Jul 05 2011

(PARI) is(n)=Set(digits(n)%2)==[1] \\ Charles R Greathouse IV, Jul 06 2017

CROSSREFS

Similar to but different from A066640.

Subsequence of A059708. Cf. A005408, A010879, A014263, A046034, A084545, A089581, A084984, A001743, A001744, A202267, A202268, A196564.

Cf. A192107.

Cf. A030096 (primes).

Subsequence of A225985.

Sequence in context: A074775 A225105 A143451 * A066640 A137507 A061808

Adjacent sequences:  A014258 A014259 A014260 * A014262 A014263 A014264

KEYWORD

nonn,base,easy,look

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Robert G. Wilson v, Oct 18 2002

Examples and crossrefs added by Hieronymus Fischer, Jun 06 2012

STATUS

approved

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Last modified January 18 21:54 EST 2019. Contains 319282 sequences. (Running on oeis4.)