The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A359794 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A359794

Union of odd numbers and numbers with an odd 2-adic valuation.
(history; published version)

#9 by Michael De Vlieger at Wed Jan 25 22:23:05 EST 2023

STATUS

proposed

approved

#8 by Amiram Eldar at Wed Jan 25 15:10:56 EST 2023

STATUS

editing

proposed

#7 by Amiram Eldar at Wed Jan 25 15:10:47 EST 2023

COMMENTS

The asymptotic density of this sequence is 5/6. - Amiram Eldar, Jan 25 2023

MATHEMATICA

Select[Range[100], OddQ[#] || OddQ[IntegerExponent[#, 2]] &] (* Amiram Eldar, Jan 25 2023 *)

STATUS

proposed

editing

#6 by Antti Karttunen at Wed Jan 25 15:02:41 EST 2023

STATUS

editing

proposed

#5 by Antti Karttunen at Wed Jan 25 15:00:16 EST 2023

COMMENTS

Number Numbers k for which the parities of k and A048675(k) differ.

#4 by Antti Karttunen at Wed Jan 25 14:57:56 EST 2023

COMMENTS

A multiplicative semigroup; if m and n are in the sequence then so is m*n.

#3 by Antti Karttunen at Wed Jan 25 14:56:18 EST 2023

COMMENTS

A multiplicative semigroup; if m and n are in the sequence then so is m*n.

CROSSREFS

Union of A005408 and A036554.

Cf. A048675, A359832 (characteristic function).

#2 by Antti Karttunen at Wed Jan 25 14:53:10 EST 2023

NAME

allocated for Antti KarttunenUnion of odd numbers and numbers with an odd 2-adic valuation.

DATA

1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89, 90, 91, 93, 94

OFFSET

1,2

COMMENTS

Numbers not of the form (2*m - 1)*4^k where m >= 1, k >= 1.

Number k for which the parities of k and A048675(k) differ.

PROG

(PARI) isA359794(n) = A359832(n);

CROSSREFS

Complement of A108269.

Cf. A359832 (characteristic function).

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Jan 25 2023

STATUS

approved

editing

#1 by Antti Karttunen at Fri Jan 13 06:41:21 EST 2023

NAME

allocated for Antti Karttunen

KEYWORD

allocated

STATUS

approved