cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A303367 Numbers equal to the determinant of a circulant matrix based on the base-7 digits of n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 27, 81, 133, 143, 144, 152, 190, 209, 250, 1125, 8569, 10934, 16401, 237568, 362306, 391257, 695751, 723260, 5294625, 6056974, 6332291, 6523631, 6669475, 11128547, 12486285, 17417491, 18682225, 19429514, 19781014, 20924092, 21671381
Offset: 1

Views

Author

M. F. Hasler, May 05 2018

Keywords

Comments

Base 7 variant of A219327. See A303366 .. A303369 for other bases.

Examples

			133 is in the sequence because 133 = 250[7] (in base 7) and 133 = det [2,5,0; 0,2,5; 5,0,2].

Crossrefs

Cf. A303366 (base 6), A303368 (base 8), A303369 (base 9), A219327 (base 10).

Programs

  • PARI
    (c(v)=abs(matdet(matrix(#v,#v,i,j,v[(j-i)%#v+1]))));for(n=1,oo,n==c(digits(n,7))&&print1(n","))

Extensions

a(25)-a(37) from Giovanni Resta, May 07 2018

A303368 Numbers equal to the determinant of a circulant matrix based on the base-8 digits of n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 21, 133, 432, 525, 1200, 1456, 1904, 4774, 24583, 281048, 289820, 333293, 420239, 428752, 430686, 437554, 500380, 500888, 736600, 941578, 984377, 1027176, 1069975, 1112774, 1155573, 1662216, 1776201, 2087008, 3212235, 7928375, 8131725
Offset: 1

Views

Author

M. F. Hasler, May 05 2018

Keywords

Comments

Base 8 variant of A219327.

Crossrefs

Cf. A303367 (base 7), A303369 (base 9), A219327 (base 10).

Programs

  • PARI
    (c(v)=abs(matdet(matrix(#v,#v,i,j,v[(j-i)%#v+1]))));for(n=1,oo,n==c(digits(n,8))&&print1(n","))

Extensions

a(33)-a(38) from Giovanni Resta, May 07 2018

A303366 Numbers equal to the determinant of a circulant matrix based on the base-6 digits of n.

Original entry on oeis.org

1, 2, 3, 4, 5, 320, 1936, 2761, 3421, 3732, 4043, 4354, 1697296, 2121620, 2970268, 3076349, 5222639, 8979475, 41657517, 63095140, 110416495, 488553143, 646839439, 1066194997, 1209597525, 1803581465, 1861934400, 2019744271, 2691271467, 2842031031, 3052726590, 7100897730, 10806417998
Offset: 1

Views

Author

M. F. Hasler, May 05 2018

Keywords

Comments

Base 6 variant of A219327. See A303367 .. A303369 for other bases.

Examples

			320 is in the sequence because 320 = 1252[6] (in base 6) and 320 = det [1,2,5,2; 2,1,2,5; 5,2,1,2; 2,5,2,1].

Crossrefs

Cf. A303367 (base 7), A303368 (base 8), A303369 (base 9), A219327 (base 10).

Programs

  • Mathematica
    Select[Range[5000],#==Det[NestList[RotateRight,IntegerDigits[#,6],IntegerLength[#,6]-1]]&] (* The program generates the first 12 terms of the sequence. *) (* Harvey P. Dale, Mar 11 2024 *)
  • PARI
    (c(v)=abs(matdet(matrix(#v,#v,i,j,v[(j-i)%#v+1]))));for(n=1,oo,n==c(digits(n,6))&&print1(n","))

Extensions

a(13)-a(33) from Giovanni Resta, May 07 2018

A305371 The binary expansions of b(n+1) and b(n) are required to have 1's in common at exactly the positions where a(n) has a 1 in its binary expansion, where b() is A305369.

Original entry on oeis.org

1, 2, 0, 4, 1, 8, 0, 6, 1, 16, 0, 10, 1, 20, 0, 32, 1, 12, 0, 18, 1, 36, 0, 24, 1, 34, 0, 28, 1, 64, 0, 14, 1, 48, 0, 66, 1, 40, 0, 22, 1, 72, 0, 38, 1, 80, 0, 42, 1, 68, 0, 26, 1, 96, 0, 30, 1, 128, 0, 44, 1, 82, 0, 132, 1, 50, 0, 76, 1, 130, 0, 52, 1, 74, 0, 144, 1, 46, 0, 192, 1, 54, 0, 136, 1, 70, 0, 56, 1, 134
Offset: 1

Views

Author

N. J. A. Sloane, Jun 02 2018

Keywords

Comments

The definition here is a consequence (or restatement) of the definition of A305369. The connection with A109812 is at present only an empirical observation.

Examples

			a(8) = 6 = 110_2, which expresses the fact that A305369(8) = 6 = 110_2 and A303369(9) = 7 = 111_2 have binary expensions whose common 1's are 110_2.

Links

Crossrefs

Cf. A305369, A109812.

Formula

Empirical: For k >= 0, a(4k+1)=1, a(4k+3)=0; for k >= 1, a(2k)=2*A109812(k).
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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