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A054684
Numbers whose sum of digits is odd.
13
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
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
KEYWORD
nonn,easy,base
AUTHOR
Odimar Fabeny, Apr 19 2000
EXTENSIONS
More terms from James A. Sellers, Apr 19 2000
STATUS
approved