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Title: Odd Number -- from Wolfram MathWorld

Open Graph Title: Odd Number -- from Wolfram MathWorld

X Title: Odd Number -- from Wolfram MathWorld

Description: An odd number is an integer of the form n=2k+1, where k is an integer. The odd numbers are therefore ..., -3, -1, 1, 3, 5, 7, ... (OEIS A005408), which are also the gnomonic numbers. Integers which are not odd are called even. Odd numbers leave a remainder of 1 when divided by two, i.e., the congruence n=1 (mod 2) holds for odd n. The oddness of a number is called its parity, so an odd number has parity 1, while an even number has parity 0. The generating function for the odd numbers is ...

Open Graph Description: An odd number is an integer of the form n=2k+1, where k is an integer. The odd numbers are therefore ..., -3, -1, 1, 3, 5, 7, ... (OEIS A005408), which are also the gnomonic numbers. Integers which are not odd are called even. Odd numbers leave a remainder of 1 when divided by two, i.e., the congruence n=1 (mod 2) holds for odd n. The oddness of a number is called its parity, so an odd number has parity 1, while an even number has parity 0. The generating function for the odd numbers is ...

X Description: An odd number is an integer of the form n=2k+1, where k is an integer. The odd numbers are therefore ..., -3, -1, 1, 3, 5, 7, ... (OEIS A005408), which are also the gnomonic numbers. Integers which are not odd are called even. Odd numbers leave a remainder of 1 when divided by two, i.e., the congruence n=1 (mod 2) holds for odd n. The oddness of a number is called its parity, so an odd number has parity 1, while an even number has parity 0. The generating function for the odd numbers is ...

Opengraph URL: https://mathworld.wolfram.com/OddNumber.html

X: @WolframResearch

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Domain: mathworld.wolfram.com

DC.TitleOdd Number
DC.CreatorWeisstein, Eric W.
DC.DescriptionAn odd number is an integer of the form n=2k+1, where k is an integer. The odd numbers are therefore ..., -3, -1, 1, 3, 5, 7, ... (OEIS A005408), which are also the gnomonic numbers. Integers which are not odd are called even. Odd numbers leave a remainder of 1 when divided by two, i.e., the congruence n=1 (mod 2) holds for odd n. The oddness of a number is called its parity, so an odd number has parity 1, while an even number has parity 0. The generating function for the odd numbers is ...
DC.Date.Modified2003-09-04
DC.Subject11A
DC.RightsCopyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement.
DC.Formattext/html
DC.Identifierhttps://mathworld.wolfram.com/OddNumber.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
DC.Relation.IsPartOfhttps://mathworld.wolfram.com/
DC.TypeText
Last-Modified2003-09-04
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og:typewebsite
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congruencehttps://mathworld.wolfram.com/Congruence.html
parityhttps://mathworld.wolfram.com/Parity.html
parityhttps://mathworld.wolfram.com/Parity.html
parityhttps://mathworld.wolfram.com/Parity.html
generating functionhttps://mathworld.wolfram.com/GeneratingFunction.html
even numberhttps://mathworld.wolfram.com/EvenNumber.html
evenhttps://mathworld.wolfram.com/EvenNumber.html
evenhttps://mathworld.wolfram.com/EvenNumber.html
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Gnomonic Numberhttps://mathworld.wolfram.com/GnomonicNumber.html
Nicomachus's Theoremhttps://mathworld.wolfram.com/NicomachussTheorem.html
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Odd Perfect Numberhttps://mathworld.wolfram.com/OddPerfectNumber.html
Odd Primehttps://mathworld.wolfram.com/OddPrime.html
Parityhttps://mathworld.wolfram.com/Parity.html
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is 5 an odd number ? https://www.wolframalpha.com/input/?i=is+5+an+odd+number+%3
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