A054684 Numbers whose sum of digits is odd.

1, 3, 5, 7, 9, 10, 12, 14, 16, 18, 21, 23, 25, 27, 29, 30, 32, 34, 36, 38, 41, 43, 45, 47, 49, 50, 52, 54, 56, 58, 61, 63, 65, 67, 69, 70, 72, 74, 76, 78, 81, 83, 85, 87, 89, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 111, 113, 115, 117, 119, 120, 122, 124, 126, 128, 131

Offset

1,2

Comments

Union of A179083 and A179085; A179081(a(n)) = 1. - Reinhard Zumkeller, Jun 28 2010

Equivalently, integers with an odd number of odd digits. - Bernard Schott, Nov 06 2022

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Index entries for 10-automatic sequences.

Index entries for Colombian or self numbers and related sequences

Formula

a(n) = n * 2 - 1 for the first 5 numbers; a(n) = n * 2 for the second 5 numbers.

From Robert Israel, Jun 27 2017: (Start)

a(n) = 2*n-2 if floor((n-1)/5) is in the sequence, 2*n-1 if not.

G.f. g(x) satisfies g(x) = (1-x)*(1+x+x^2+x^3+x^4)^2*g(x^10)/x^9 + x^2*(2+x^4+3*x^5-x^9+3*x^10)/((1-x)*(1+x^5))^2.

(End)

Example

1, 3, 5, 7, 9, 10(1), 12(3), 14(5), 16(7), 18(9), 21(3) and so on.

Maple

[seq(`if`(convert(convert(2*n-1, base, 10), `+`)::odd, 2*n-1, 2*n-2), n=1..501)];

Mathematica

Select[Range[200], OddQ[Total[IntegerDigits[#]]]&] (* Harvey P. Dale, Nov 27 2021 *)

Prog

(PARI) is(n)=my(d=digits(n)); sum(i=1, #d, d[i])%2 \\ Charles R Greathouse IV, Aug 09 2013
(PARI) isok(m) = sumdigits(m) % 2; \\ Michel Marcus, Nov 06 2022
(PARI) a(n) = n=2*(n-1); n + !(sumdigits(n)%2); \\ Kevin Ryde, Nov 07 2022
(Python)
def ok(n): return sum(map(int, str(n)))&1
print([k for k in range(132) if ok(k)]) # Michael S. Branicky, Nov 06 2022

Crossrefs

Cf. A054683, A137233 (number of n-digits terms).

Cf. A356929 (even number of even digits).

A294601 (exactly one odd decimal digit) is a subsequence.

Sequence in context: A287774 A308412 A327254 * A294601 A376692 A358529

Adjacent sequences: A054681 A054682 A054683 * A054685 A054686 A054687

Keyword

nonn,easy,base

Author

Odimar Fabeny, Apr 19 2000

Extensions

More terms from James A. Sellers, Apr 19 2000

Status

approved