A047332 -id:A047332 - cp's OEIS frontend

A225003 Duplicate of A047332.

23, 2, 3, 5, 6, 7, 9, 10, 12, 13, 14, 16, 17, 19, 20, 21, 23, 24, 26, 27, 28, 30, 31, 33, 34, 35, 37, 38, 40, 41, 42, 44, 45, 47, 48, 49, 51, 52, 54, 55, 56, 58, 59, 61, 62, 63, 65, 66, 68, 69, 70, 72, 73, 75, 76, 77, 79, 80, 82, 83, 84, 86, 87, 89, 90, 91, 93

Offset: 1

T. D. Noe, Apr 26 2013

dead

th = E^(5/7); t = Table[Floor[1/FractionalPart[th^(1/n)]], {n, 100}]

A085269 Integer part of the conversion from centimeters to inches.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 14, 14, 14, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 23, 24, 24, 24, 25, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30

Offset: 0

Cino Hilliard, Aug 12 2003

2.54 = 127/50. - Eric Desbiaux, Nov 16 2008

Paolo Xausa, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, order 128.

Cf. A224233, A085270.

Floor[Range[0, 100]*100/254] (* Paolo Xausa, Jul 16 2025 *)

PARI
```
a(n) = floor(n*100/254);
```

a(n) = floor(n/2.54).

Eric Desbiaux suggested (Apr 19 2008) that A047332(n)-A080686(n) =? a(n-1), but R. J. Mathar points out that this is only true for the first 23 terms and so is nothing more than a coincidence. - N. J. A. Sloane, Apr 26 2008

Corrected by T. D. Noe, Nov 02 2006

A224996 a(n) = floor(1/f(x^(1/n))) for x = 2, where f computes the fractional part.

Original entry on oeis.org

2, 3, 5, 6, 8, 9, 11, 12, 13, 15, 16, 18, 19, 21, 22, 24, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 39, 41, 42, 44, 45, 47, 48, 49, 51, 52, 54, 55, 57, 58, 60, 61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 75, 77, 78, 80, 81, 83, 84, 86, 87, 88, 90, 91, 93, 94, 96, 97

Offset: 2

T. D. Noe, Apr 26 2013

First denominator of continued fraction representing 2^(1/n): [1,a(n),....] so that 1+1/a(n) is first convergent for 2^(1/n). - Carmine Suriano, Apr 29 2014

a(n) is the largest integer y that satisfies (y+1)^n - y^n >= y^n, or equivalently (y+1)^n >= 2*y^n. - Charles Kusniec, Jan 19 2025

Melvyn B. Nathanson, On the fractional parts of roots of positive real numbers, Amer. Math. Monthly, 120 (2013), 409-429.

Cf. A224995, A224997, A224998, A001651, A047211, A047203, A047290, A047332.

Cf. A078607 (the smallest integer y that satisfies (y+1)^n - y^n < y^n).

th = 2; t = Table[Floor[1/FractionalPart[th^(1/n)]], {n, 2, 100}]

a(n) = floor(n/log(2)-1/2). - Andrey Zabolotskiy, Dec 01 2017

A224995 Floor(1/f(x^(1/n))) for x = 3/2, where f computes the fractional part.

Original entry on oeis.org

2, 4, 6, 9, 11, 14, 16, 19, 21, 24, 26, 29, 31, 34, 36, 38, 41, 43, 46, 48, 51, 53, 56, 58, 61, 63, 66, 68, 71, 73, 75, 78, 80, 83, 85, 88, 90, 93, 95, 98, 100, 103, 105, 108, 110, 112, 115, 117, 120, 122, 125, 127, 130, 132, 135, 137, 140, 142, 145, 147, 149

Offset: 1

T. D. Noe, Apr 26 2013

Melvyn B. Nathanson, On the fractional parts of roots of positive real numbers, Amer. Math. Monthly, 120 (2013), 409-429.

Cf. A224996, A224997, A224998, A001651, A047211, A047203, A047290, A047332.

th = 3/2; t = Table[Floor[1/FractionalPart[th^(1/n)]], {n, 100}]

a(n) = floor(n/log(3/2)-1/2) for n>1. - Andrey Zabolotskiy, Dec 01 2017

A224997 Floor(1/f(x^(1/n))) for x = 17, where f computes the fractional part.

Original entry on oeis.org

8, 1, 32, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 25

Offset: 2

T. D. Noe, Apr 26 2013

Melvyn B. Nathanson, On the fractional parts of roots of positive real numbers, Amer. Math. Monthly, 120 (2013), 409-429.

Cf. A224995, A224996, A224998, A001651, A047211, A047203, A047290, A047332.

th = 17; t = Table[Floor[1/FractionalPart[th^(1/n)]], {n, 2, 100}]

a(n) = floor(n/log(17)-1/2) for n>7. - Andrey Zabolotskiy, Dec 01 2017

A224998 Floor(1/f(x^(1/n))) for x = Pi, where f computes the fractional part.

Original entry on oeis.org

7, 1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 9, 10, 11, 12, 13, 14, 15, 16, 16, 17, 18, 19, 20, 21, 22, 23, 23, 24, 25, 26, 27, 28, 29, 30, 30, 31, 32, 33, 34, 35, 36, 37, 37, 38, 39, 40, 41, 42, 43, 44, 44, 45, 46, 47, 48, 49, 50, 51, 51, 52, 53, 54, 55, 56, 57, 58, 58

Offset: 1

T. D. Noe, Apr 26 2013

Melvyn B. Nathanson, On the fractional parts of roots of positive real numbers, Amer. Math. Monthly, 120 (2013), 409-429.

Cf. A224995, A224996, A224997, A001651, A047211, A047203, A047290, A047332.

th = Pi; t = Table[Floor[1/FractionalPart[th^(1/n)]], {n, 100}]

a(n) = floor(n/log(Pi)-1/2) for n>4. - Andrey Zabolotskiy, Dec 01 2017

A382657 Number of minimum total dominating sets in the n-Goldberg graph.

Original entry on oeis.org

16, 277, 10, 2386, 28, 33301, 360, 10, 4334, 60, 67288, 728, 10, 9856, 102, 150750, 1292, 10, 19222, 154, 299368, 2124, 10, 34112, 216, 549276, 3306, 10, 56730, 288, 951456, 4930, 10, 89916, 370, 1576202, 7098, 10, 137268, 462, 2518596, 9922, 10, 203274, 564, 3905148, 13524, 10

Offset: 3

Eric W. Weisstein, Apr 02 2025

For n > 3, the total domination number is given by 2*floor((7*n+4)/5) = 2*A047332(n+1). For n = 3, the total domination number is 9. - Andrew Howroyd, May 24 2025

Andrew Howroyd, Table of n, a(n) for n = 3..1000
Eric Weisstein's World of Mathematics, Goldberg Graph.
Eric Weisstein's World of Mathematics, Minimum Total Dominating Set.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,9, 0,0,0,0,-36, 0,0,0,0,84, 0,0,0,0,-126, 0,0,0,0,126, 0,0,0,0,-84, 0,0,0,0,36, 0,0,0,0,-9, 0,0,0,0,1).

Cf. A382431.

a(n) = { my(m=n\5+1,r=-n%5); if(n<=8, [16, 277, 10, 2386, 28, 33301][n-2], if(r<=2, if(r==0, 10, n*if(r==1, (m + 13)*(m^2 + 2*m + 24)/12, (m^7 + 70*m^6 + 1750*m^5 + 39340*m^4 + 525889*m^3 + 2944270*m^2 + 15922920*m + 12216960)/20160)), n*if(r==3, (m + 2), (m^5 + 35*m^4 + 365*m^3 + 5485*m^2 + 21114*m + 16200)/360) )) } \\ Andrew Howroyd, May 24 2025

a(5*n) = 10.
From Andrew Howroyd, May 24 2025: (Start)
a(5*n-1) = (5*n-1)*(n + 13)*(n^2 + 2*n + 24)/12 for n >= 2;
a(5*n-2) = (5*n-2)*(n^7 + 70*n^6 + 1750*n^5 + 39340*n^4 + 525889*n^3 + 2944270*n^2 + 15922920*n + 12216960)/20160 for n >= 3;
a(5*n-3) = (5*n-3)*(n + 2) for n >= 2;
a(5*n-4) = (5*n-4)*(n^5 + 35*n^4 + 365*n^3 + 5485*n^2 + 21114*n + 16200)/360 for n >= 3. (End)

a(8)-a(12) from Eric W. Weisstein, May 11 2025

a(13) onwards from Andrew Howroyd, May 24 2025

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A225003 Duplicate of A047332.

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A085269 Integer part of the conversion from centimeters to inches.

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A224996 a(n) = floor(1/f(x^(1/n))) for x = 2, where f computes the fractional part.

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A224995 Floor(1/f(x^(1/n))) for x = 3/2, where f computes the fractional part.

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A224997 Floor(1/f(x^(1/n))) for x = 17, where f computes the fractional part.

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A224998 Floor(1/f(x^(1/n))) for x = Pi, where f computes the fractional part.

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A382657 Number of minimum total dominating sets in the n-Goldberg graph.

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