Hans Isdahl - cp's OEIS frontend

A214329 Complement of A214328.

2, 3, 5, 6, 8, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 29, 30, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85, 86, 88, 89, 90, 91, 93, 94, 96, 97, 98, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109

Offset: 1

N. J. A. Sloane, Jul 26 2012, following a suggestion from Hans Isdahl, Apr 19 2012

nonn

Numbers that are the sum of 2 or 3 nonzero squares. - Altug Alkan, Jan 13 2016

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A000404, A000408, A004214, A018825, A214328.

is2(n) = {for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2))}
is3(n) = {my(a, b) ; a=1; while(a^2+1Altug Alkan, Jan 13 2016

A214328 Intersection of A004214 and A018825.

Original entry on oeis.org

1, 4, 7, 15, 16, 23, 28, 31, 39, 47, 55, 60, 63, 64, 71, 79, 87, 92, 95, 103, 111, 112, 119, 124, 127, 135, 143, 151, 156, 159, 167, 175, 183, 188, 191, 199, 207, 215, 220, 223, 231, 239, 240, 247, 252, 255, 256, 263, 271, 279, 284, 287, 295, 303, 311, 316, 319, 327, 335, 343, 348, 351, 359, 367, 368, 375, 380, 383, 391, 399, 407, 412, 415, 423, 431, 439

Offset: 1

N. J. A. Sloane, Jul 26 2012, following a suggestion from Hans Isdahl, Apr 19 2012

nonn

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A000408, A004214, A000404, A018825, A214329.

a(n) ~ 6 * n. - Bill McEachen, Mar 24 2024

A134934 a(n) = (14*n+1)^2.

Original entry on oeis.org

1, 225, 841, 1849, 3249, 5041, 7225, 9801, 12769, 16129, 19881, 24025, 28561, 33489, 38809, 44521, 50625, 57121, 64009, 71289, 78961, 87025, 95481, 104329, 113569, 123201, 133225, 143641, 154449, 165649, 177241, 189225, 201601, 214369, 227529, 241081

Offset: 0

Hans Isdahl, Jan 26 2008

Number of rats in population after n years, starting with one rat at year 0 (see A016754 for more details).

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Sequences of the form (m*n+1)^2: A000012 (m=0), A000290 (m=1), A016754 (m=2), A016778 (m=3), A016814 (m=4), A016862 (m=5), A016922 (m=6), A016994 (m=7), A017078 (m=8), A017174 (m=9), A017282 (m=10), A017402 (m=11), A017534 (m=12), this sequence (m=14).

Cf. A016754.

[(14*n+1)^2: n in [0..50]]; // Vincenzo Librandi, Sep 06 2011

(14*Range[0,50]+1)^2 (* G. C. Greubel, Dec 24 2022 *)

a(n)=(14*n+1)^2 \\ Charles R Greathouse IV, Jun 17 2017

[(14*n+1)^2 for n in range(51)] # G. C. Greubel, Dec 24 2022

O.g.f.: (1+222*x+169*x^2)/(1-x)^3 = 169/(1-x) - 560/(1-x)^2 + 392/(1-x)^3. - R. J. Mathar, Jan 31 2008
a(n) = A016754(7*n).
E.g.f.: (1 + 224*x + 196*x^2)*exp(x). - G. C. Greubel, Dec 24 2022

A131062 Rounded frequencies of notes in a Pythagorean scale, starting with 260.7 Hertz for a C.

Original entry on oeis.org

261, 293, 330, 348, 391, 440, 495, 521, 587, 660, 695, 782, 880, 990, 1043, 1173, 1320, 1391, 1564, 1760, 1980, 2086

Offset: 1

Hans Isdahl, Sep 24 2007

nonn

The approximate value of 260.7 Hz for the C corresponds to 16/27 * 440 Hz. The frequencies correspond to the ratios [1/1, 9/8, 81/64, 4/3, 3/2, 27/16, 243/128, 2/1].

Wikipedia, Just intonation - Pythagorean tuning.
Wikipedia, Pythagorean tuning.
Index entries for sequences related to music.

Cf. A131071 for the same scale including half-tones.
Cf. A071831/A071832 = A071833/24. - M. F. Hasler, Jun 14 2012
Cf. A101285.

Value of a(8) corrected, sequence extended to 3 octaves and comments added by M. F. Hasler (following suggestions by Franklin T. Adams-Watters and Charles R Greathouse IV), Oct 05 2011

A131071 12-note scale in Hertz (rounded to integers).

Original entry on oeis.org

261, 275, 293, 309, 330, 348, 366, 391, 412, 440, 464, 495, 521

Offset: 1

Hans Isdahl, Sep 24 2007

nonn

Wikipedia, Pythagorean tuning.
Index entries for sequences related to music.

Cf. A131062 for the corresponding C major scale. [M. F. Hasler, Oct 07 2011]

Cf. A214832.

The scale involves 9/8 and 256/243 as fractions and the start is A = 440 Hz.

The initial term (rounded frequency of the C) is calculated as 16/27 * 440 Hz = 260.74 Hz, cf. the Wikipedia page on Pythagorean tuning for the ratios of the frequencies. - M. F. Hasler, Oct 07 2011

A131098 Partial sums of A151798.

Original entry on oeis.org

1, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 123, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, 179, 183, 187, 191, 195, 199, 203, 207, 211, 215, 219, 223, 227, 231, 235, 239

Offset: 1

Hans Isdahl, Sep 24 2007

1 together with A004767. - Omar E. Pol, Feb 23 2014

			g.f. = x + 3*x^2 + 7*x^3 + 11*x^4 + 15*x^5 + 19*x^6 + 23*x^7 + 27*x^8 + ...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
David Applegate, The movie version
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A151798, A004767.

I:=[1,3,7]; [n le 3 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..70]]; // Vincenzo Librandi, Feb 25 2014

CoefficientList[Series[(x + 2 x^2 + 1)/(x - 1)^2, {x, 0, 80}], x] (* Vincenzo Librandi, Feb 25 2014 *)
LinearRecurrence[{2,-1},{1,3,7},70] (* Harvey P. Dale, Jan 03 2023 *)

A131098(n)=abs(4*n-5) \\ M. F. Hasler, Apr 27 2018

a(1) = 1, a(n) = 4*n - 5 for n >= 2. - Jaroslav Krizek, Aug 15 2009
G.f.: x*(x+2*x^2+1)/(x-1)^2. - R. J. Mathar, Dec 08 2010
E.g.f.: exp(x)*(4*x - 5) + 5 + 2*x. - Stefano Spezia, Mar 21 2025

Edited by N. J. A. Sloane, Jun 29 2009

A118263 a(3n) = 2^n, a(3n+1) = 3^n, a(3n+2) = 4^n.

Original entry on oeis.org

1, 1, 1, 2, 3, 4, 4, 9, 16, 8, 27, 64, 16, 81, 256, 32, 243, 1024, 64, 729, 4096, 128, 2187, 16384, 256, 6561, 65536, 512, 19683, 262144, 1024, 59049, 1048576, 2048, 177147, 4194304, 4096, 531441, 16777216, 8192, 1594323, 67108864, 16384, 4782969

Offset: 0

Hans Isdahl, Sep 20 2007

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,9,0,0,-26,0,0,24).

Table[{2^Floor[n/3], 3^Floor[n/3], 4^Floor[n/3]}[[Mod[n, 3] + 1]], {n, 0, 100}] (* Olivier Gérard, Sep 20 2007 *)
LinearRecurrence[{0,0,9,0,0,-26,0,0,24},{1,1,1,2,3,4,4,9,16},60] (* Harvey P. Dale, Jan 30 2021 *)

From R. J. Mathar, Mar 01 2010: (Start)
a(n) = 9*a(n-3) - 26*a(n-6) + 24*a(n-9).
G.f.: -(1+x+x^2-7*x^3-6*x^4-5*x^5+12*x^6+8*x^7+6*x^8) / ((3*x^3-1) * (2*x^3-1) * (4*x^3-1)). (End)

More terms from Olivier Gérard, Sep 20 2007

cp's OEIS Frontend

User: Hans Isdahl

A214329 Complement of A214328.

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A214328 Intersection of A004214 and A018825.

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A134934 a(n) = (14*n+1)^2.

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A131062 Rounded frequencies of notes in a Pythagorean scale, starting with 260.7 Hertz for a C.

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A131071 12-note scale in Hertz (rounded to integers).

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A131098 Partial sums of A151798.

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A118263 a(3n) = 2^n, a(3n+1) = 3^n, a(3n+2) = 4^n.

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