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A054684
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Numbers whose sum of digits is odd.
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13
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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
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OFFSET
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1,2
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COMMENTS
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Equivalently, integers with an odd number of odd digits. - Bernard Schott, Nov 06 2022
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LINKS
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FORMULA
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a(n) = n * 2 - 1 for the first 5 numbers; a(n) = n * 2 for the second 5 numbers.
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)
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EXAMPLE
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1, 3, 5, 7, 9, 10(1), 12(3), 14(5), 16(7), 18(9), 21(3) and so on.
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MAPLE
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[seq(`if`(convert(convert(2*n-1, base, 10), `+`)::odd, 2*n-1, 2*n-2), n=1..501)];
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MATHEMATICA
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Select[Range[200], OddQ[Total[IntegerDigits[#]]]&] (* Harvey P. Dale, Nov 27 2021 *)
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PROG
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(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
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CROSSREFS
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Cf. A356929 (even number of even digits).
A294601 (exactly one odd decimal digit) is a subsequence.
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KEYWORD
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nonn,easy,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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