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*Odd abundant numbers below 500000 are in On-Line Encyclopedia of Integer Sequences [http://oeis.org/A005231/b005231.txt, A005231]. ...obability.org/data/files/Articles%2038/38-1-2.pdf|title=More Odd Abundant Sequences|first=|last=|date=2005|website=|publisher=JAY. SCHIFFMAN|accessdate=2017-01 ...

[[Category:Integer sequences]] ...

Let <math>p</math> be a prime integer and <math>a</math> be a positive integer. Show '''combinatorially''' that <math>a^p-a</math> is divisible by <math>p Fix <math>1\leq k\leq n</math>. How many integer sequences <math>1\leq a_1<a_2<\cdots<a_k\leq n</math> satisfy <math>a_i\equiv i\pmod ...

...the string as the [[base (mathematics)|base]] ''N''+1 representation of an integer. ...e integers, which allowed Gödel to encode not just strings of symbols, but sequences of strings as well. Given a sequence <math>x_1 x_2 x_3 ... x_n</math> of po ...

[[Category:Integer sequences]] ...

group that acts on these sequences.) Let <math>p(n)</math> be the number of sequences <math>f</math> that allow each driver to park his ...

...er''', sometimes also called a '''perfect square''', is the result of an [[integer]] [[multiplication|multiplied]] by itself. 1, 4, 9, 16 and 25 are the first ...gative) number is a square number, is that its [[square root]] is again an integer. For example, {{sqrt|9}}&nbsp;=&nbsp;3, so 9 is a square number. ...

[[Category:Integer sequences]] ...

...ble number|sociable]]. A positive integer such that every smaller positive integer is a sum of distinct divisors of it is a [[practical number]]. ...um=A000396 List of Perfect Numbers] at the On-Line Encyclopedia of Integer Sequences ...

* Count the number of ways that the nonnegative integer <math>n</math> can be written as a sum of ones and twos (in order). &= \sum_{n\ge k}g_{n-k}x^n, &\qquad (\mbox{integer }k\ge 0)\\ ...

* Count the number of ways that the nonnegative integer <math>n</math> can be written as a sum of ones and twos (in order). &= \sum_{n\ge k}g_{n-k}x^n, &\qquad (\mbox{integer }k\ge 0)\\ ...

*'''OEIS''': Link to: On-Line Encyclopedia of Integer Sequences (OEIS), where the constants are available with more details. *'''Continued fraction''': In the simple form [to integer; frac1, frac2, frac3, ...] (in brackets if periodic) ...

* Count the number of ways that the nonnegative integer <math>n</math> can be written as a sum of ones and twos (in order). &= \sum_{n\ge k}g_{n-k}x^n, &\qquad (\mbox{integer }k\ge 0)\\ ...

* Count the number of ways that the nonnegative integer <math>n</math> can be written as a sum of ones and twos (in order). &= \sum_{n\ge k}g_{n-k}x^n, &\qquad (\mbox{integer }k\ge 0)\\ ...

* Count the number of ways that the nonnegative integer <math>n</math> can be written as a sum of ones and twos (in order). &= \sum_{n\ge k}g_{n-k}x^n, &\qquad (\mbox{integer }k\ge 0)\\ ...

* Count the number of ways that the nonnegative integer <math>n</math> can be written as a sum of ones and twos (in order). &= \sum_{n\ge k}g_{n-k}x^n, &\qquad (\mbox{integer }k\ge 0)\\ ...

* Count the number of ways that the nonnegative integer <math>n</math> can be written as a sum of ones and twos (in order). &= \sum_{n\ge k}g_{n-k}x^n, &\qquad (\mbox{integer }k\ge 0)\\ ...

* Count the number of ways that the nonnegative integer <math>n</math> can be written as a sum of ones and twos (in order). &= \sum_{n\ge k}g_{n-k}x^n, &\qquad (\mbox{integer }k\ge 0)\\ ...

* Count the number of ways that the nonnegative integer <math>n</math> can be written as a sum of ones and twos (in order). &= \sum_{n\ge k}g_{n-k}x^n, &\qquad (\mbox{integer }k\ge 0)\\ ...

* Count the number of ways that the nonnegative integer <math>n</math> can be written as a sum of ones and twos (in order). &= \sum_{n\ge k}g_{n-k}x^n, &\qquad (\mbox{integer }k\ge 0)\\ ...

Fix an integer <math>t</math>, we count the number of circuits with <math>t</math> gates. We count the number of different ''sequences'' of directed edges that can be added to an empty graph on <math>n</math> v ...

We count the number of different ''sequences'' of directed edges that can be added to an empty graph on <math>n</math> v Multiplying the numbers of choices in all steps, the number of sequences of adding directed edges to an empty graph to form a rooted tree is given b ...

# <math>\Delta(k\cdot\tau_{\mathrm{mix}})\le \mathrm{e}^{-k}</math> for any integer <math>k\ge1</math>. # <math>\Delta(k\cdot\tau_{\mathrm{mix}})\le \mathrm{e}^{-k}</math> for any integer <math>k\ge1</math>. ...

# <math>\Delta(k\cdot\tau_{\mathrm{mix}})\le \mathrm{e}^{-k}</math> for any integer <math>k\ge1</math>. # <math>\Delta(k\cdot\tau_{\mathrm{mix}})\le \mathrm{e}^{-k}</math> for any integer <math>k\ge1</math>. ...

# <math>\Delta(k\cdot\tau_{\mathrm{mix}})\le \mathrm{e}^{-k}</math> for any integer <math>k\ge1</math>. # <math>\Delta(k\cdot\tau_{\mathrm{mix}})\le \mathrm{e}^{-k}</math> for any integer <math>k\ge1</math>. ...

:for some integer <math>n\ge 0</math>. State <math>i</math> '''communicates with''' state <ma ...t random sources <math>U_0',U_1',\ldots</math>. So we have two independent sequences: ...

...idable in many [[computation]]s, especially when dividing two numbers in [[integer]] or fixed-point arithmetic; when computing mathematical functions such as * replacing a decimal [[integer]] by an integer with more trailing zeros, e.g. 23,217 people by 23,200 people; or, in gener ...

:for some integer <math>n\ge 0</math>. State <math>x</math> '''communicates with''' state <ma ...t random sources <math>U_0',U_1',\ldots</math>. So we have two independent sequences: ...

:for some integer <math>n\ge 0</math>. State <math>x</math> '''communicates with''' state <ma ...t random sources <math>U_0',U_1',\ldots</math>. So we have two independent sequences: ...

:for some integer <math>n\ge 0</math>. State <math>x</math> '''communicates with''' state <ma ...t random sources <math>U_0',U_1',\ldots</math>. So we have two independent sequences: ...

:for some integer <math>n\ge 0</math>. State <math>i</math> '''communicates with''' state <ma ...t random sources <math>U_0',U_1',\ldots</math>. So we have two independent sequences: ...

...ron goes from energy state (orbit) '''b''' to energy state '''a''' (Again, sequences look backwards, but that is the way they were originally written.): We can see that <math>n</math> must be an integer. This means that the particle can only have special energy values and cann ...