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.

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A111952 a(n) = 3*n mod 7.

Original entry on oeis.org

0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1
Offset: 0

Views

Author

Paul Barry, Aug 22 2005

Keywords

Comments

Period 7: repeat [0, 3, 6, 2, 5, 1, 4].
Draw a regular heptagon with vertices labeled 0..6 going clockwise. Choose any seven consecutive values of a(n) and connect the corresponding vertices in that order with straight lines. This results in a clockwise-inscribed seven-pointed star that remains unbroken during construction. - Wesley Ivan Hurt, Apr 10 2015

Links

Crossrefs

Cf. A022264.

Programs

Formula

G.f.: (3*x+6*x^2+2*x^3+5*x^4+x^5+4*x^6)/(1-x^7).
a(n) = mod(n*(7*n-1)/2, 7) = mod(A022264(n), 7).
Recurrence: a(n) = a(n-7) for n > 6. - Wesley Ivan Hurt, Apr 10 2015
a(n) = (21 + 4*(n mod 7) - 3*((n+1) mod 7) + 4*((n+2) mod 7) - 3*((n+3) mod 7) + 4*((n+4) mod 7) - 3*((n+5) mod 7) - 3*((n+6) mod 7))/7. - Wesley Ivan Hurt, Dec 23 2016
a(n) = A010876(3*n). - R. J. Mathar, Jan 15 2021

A114448 Array a(n,k) = n^k (mod k) read by antidiagonals (k>=1, n>=1).

Original entry on oeis.org

0, 0, 1, 0, 0, 1, 0, 1, 2, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 1, 0, 0, 2, 0, 3, 4, 1, 0, 1, 0, 1, 4, 3, 2, 1, 0, 0, 1, 0, 0, 4, 3, 0, 1, 0, 1, 2, 1, 1, 1, 4, 1, 8, 1, 0, 0, 0, 0, 2, 0, 5, 0, 0, 4, 1, 0, 1, 1, 1, 3, 1, 6, 1, 1, 9, 2, 1, 0, 0, 2, 0, 4, 4, 0, 0, 8, 6, 3, 4, 1, 0, 1, 0, 1, 0, 3, 1, 1, 0, 5, 4, 9, 2, 1
Offset: 1

Views

Author

Leroy Quet, Feb 14 2006

Keywords

Comments

Alternate description: triangular array a(n, k) = n^k (mod k) read by rows (n > 1, 0 < k < n). This is equivalent because a(n, k) = a(n-k, k). - David Wasserman, Jan 25 2007

Examples

			2^6 = 64 and 64 (mod 6) is 4. So a(2,6) = 4.

Crossrefs

Cf. A051127, A051128, A094263. Transpose of A060154. First 13 rows are A057427(n-1), A015910, A066601, A066602, A066603, A066604, A066438, A066439, A066440, A056969, A066441, A066442, A116609. First 12 columns are A000004, A000035, A010872, A000035, A010874, A070431, A010876, A000035, A021559(n+1), A008959, A010880, A070435.

Programs

  • Mathematica
    a[n_, k_] := Mod[n^k, k]; Table[a[n - k + 1, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Dec 12 2012 *)

Extensions

More terms from David Wasserman, Jan 25 2007

A277545 a(n) = n/7^m mod 7, where 7^m is the greatest power of 7 that divides n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 1, 1, 2, 3, 4, 5, 6, 2, 1, 2, 3, 4, 5, 6, 3, 1, 2, 3, 4, 5, 6, 4, 1, 2, 3, 4, 5, 6, 5, 1, 2, 3, 4, 5, 6, 6, 1, 2, 3, 4, 5, 6, 1, 1, 2, 3, 4, 5, 6, 1, 1, 2, 3, 4, 5, 6, 2, 1, 2, 3, 4, 5, 6, 3, 1, 2, 3, 4, 5, 6, 4, 1, 2, 3, 4, 5, 6, 5, 1, 2
Offset: 1

Views

Author

Clark Kimberling, Oct 19 2016

Keywords

Comments

a(n) is the rightmost nonzero digit in the base 7 expansion of n.

Examples

			a(9) = (9/7 mod 7) = 2.

Links

Crossrefs

Cf. A010876, A242603.

Programs

  • Mathematica
    Table[Mod[n/7^IntegerExponent[n, 7], 7], {n, 1, 160}]
  • PARI
    a(n) = n/7^valuation(n, 7) % 7; \\ Michel Marcus, Oct 20 2016

Formula

a(n) = A242603(n) mod 7. - Michel Marcus, Oct 20 2016

A038138 Order of n (mod 7).

Original entry on oeis.org

0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0
Offset: 0

Views

Author

Felice Russo

Keywords

Links

Crossrefs

Cf. A010876, A218256.

Programs

  • Magma
    [Modorder(n,7): n in [0..110]]; // Bruno Berselli, Mar 22 2016
  • Mathematica
    ReplacePart[Table[MultiplicativeOrder[n, 7], {n, 105}], List /@ Range[7, 105, 7] -> 0] (* Alonso del Arte, Mar 23 2016 *)
PadRight[{},120,{0,1,3,6,3,6,2}] (* Harvey P. Dale, Apr 26 2020 *)
  • PARI
    a(n) = if (n % 7, znorder(Mod(n, 7)), 0); \\ Michel Marcus, Mar 22 2016
  • PARI
    x='x+O('x^200); concat(0, Vec(x*(1+3*x+6*x^2+3*x^3+6*x^4+2*x^5)/(1-x^7))) \\ Altug Alkan, Mar 23 2016

Formula

G.f.: x*(1 + 3*x + 6*x^2 + 3*x^3 + 6*x^4 + 2*x^5)/(1 - x^7). - Bruno Berselli, Mar 22 2016
a(n) = -(35*(n mod 7)^6 - 603*(n mod 7)^5 + 3860*(n mod 7)^4 - 11235*(n mod 7)^3 + 14465*(n mod 7)^2 - 6882*(n mod 7))/360. - Luce ETIENNE, Oct 20 2017

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Apr 04 2000

A126047 Exponents p of the Mersenne primes 2^p - 1 (see A000043) read mod 7.

Original entry on oeis.org

2, 3, 5, 0, 6, 3, 5, 3, 5, 5, 2, 1, 3, 5, 5, 5, 6, 4, 4, 6, 1, 1, 6, 1, 1, 4, 5, 3, 1, 1, 1, 6, 1, 6, 5, 3, 2, 5, 2, 1, 4, 5, 1, 2, 2, 4, 1, 5
Offset: 1

Views

Author

Artur Jasinski, Dec 17 2006

Keywords

Crossrefs

Cf. A000043, A010876, A126043-A126059.

Programs

  • Mathematica
    Mod[MersennePrimeExponent[Range[48]], 7] (* Amiram Eldar, Oct 14 2024 *)

Formula

a(n) = A010876(A000043(n)). - Ivan Panchenko, Apr 07 2018

Extensions

a(45)-a(46) from Ivan Panchenko, Apr 07 2018
a(47) from Ivan Panchenko, Apr 09 2018
a(48) from Amiram Eldar, Oct 14 2024
Previous Showing 31-35 of 35 results.

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