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 1-7 of 7 results.

A174996 Triangle read by rows: T(n,k) = (prime(n)-1) mod prime(k).

Original entry on oeis.org

1, 0, 2, 0, 1, 4, 0, 0, 1, 6, 0, 1, 0, 3, 10, 0, 0, 2, 5, 1, 12, 0, 1, 1, 2, 5, 3, 16, 0, 0, 3, 4, 7, 5, 1, 18, 0, 1, 2, 1, 0, 9, 5, 3, 22, 0, 1, 3, 0, 6, 2, 11, 9, 5, 28, 0, 0, 0, 2, 8, 4, 13, 11, 7, 1, 30, 0, 0, 1, 1, 3, 10, 2, 17, 13, 7, 5, 36, 0, 1, 0, 5, 7, 1, 6, 2, 17, 11, 9, 3, 40, 0, 0, 2, 0, 9, 3, 8, 4, 19, 13, 11, 5, 1, 42
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Dec 02 2010

Keywords

Examples

			The triangle starts in row n=0 with columns 1<=k<= n as:
  1;
  0, 2;
  0, 1, 4;
  0, 0, 1, 6;
  0, 1, 0, 3, 10;
  0, 0, 2, 5,  1, 12;
  0, 1, 1, 2,  5,  3, 16;
  0, 0, 3, 4,  7,  5,  1, 18;
  0, 1, 2, 1,  0,  9,  5,  3, 22;
  0, 1, 3, 0,  6,  2, 11,  9,  5, 28;

Links

Crossrefs

Cf. A006093, A173655, A173662, A174428, A174947, A175620, A176066, A177226.

Programs

  • Magma
    [(NthPrime(n)-1) mod NthPrime(k): k in [1..n], n in [1..15]]; // G. C. Greubel, Apr 12 2024
  • Mathematica
    Flatten[Table[Mod[Prime[n]-1,Prime[k]],{n,15},{k,n}]]  (* Harvey P. Dale, Apr 23 2011 *)
  • SageMath
    flatten([[(nth_prime(n)-1)%nth_prime(k) for k in range(1,n+1)] for n in range(1,16)]) # G. C. Greubel, Apr 12 2024

A174947 Triangle read by rows: T(n,k) = (prime(n)+1) mod prime(k).

Original entry on oeis.org

1, 0, 1, 0, 0, 1, 0, 2, 3, 1, 0, 0, 2, 5, 1, 0, 2, 4, 0, 3, 1, 0, 0, 3, 4, 7, 5, 1, 0, 2, 0, 6, 9, 7, 3, 1, 0, 0, 4, 3, 2, 11, 7, 5, 1, 0, 0, 0, 2, 8, 4, 13, 11, 7, 1, 0, 2, 2, 4, 10, 6, 15, 13, 9, 3, 1, 0, 2, 3, 3, 5, 12, 4, 0, 15, 9, 7, 1, 0, 0, 2, 0, 9, 3, 8, 4, 19, 13, 11, 5, 1, 0, 2, 4, 2, 0, 5, 10, 6, 21, 15, 13, 7, 3, 1
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Dec 02 2010

Keywords

Comments

Triangle read by rows: T(n,k) = Sigma(prime(n)) mod prime(k), where Sigma(prime(.)) is the sum of divisors of prime.

Examples

			Triangle begins
  1;
  0, 1;
  0, 0, 1;
  0, 2, 3, 1;
  0, 0, 2, 5, 1;
  0, 2, 4, 0, 3,  1;
  0, 0, 3, 4, 7,  5,  1;
  0, 2, 0, 6, 9,  7,  3,  1;
  0, 0, 4, 3, 2, 11,  7,  5, 1;
  0, 0, 0, 2, 8,  4, 13, 11, 7, 1;

Links

Crossrefs

Cf. A174428, A173655, A173662, A174996, A175620, A177226.

Programs

  • Magma
    [(1+NthPrime(n)) mod NthPrime(k): k in [1..n], n in [1..15]]; // G. C. Greubel, Apr 10 2024
  • Mathematica
    Table[Mod[1+Prime[n], Prime[k]], {n,15}, {k,n}]//Flatten (* G. C. Greubel, Apr 10 2024 *)
  • PARI
    trga(nrows) = {for (n=1, nrows, for (k=1, n, print1(sigma(prime(n)) % prime(k), ", ");); print(););} \\ Michel Marcus, Apr 11 2013
  • SageMath
    flatten([[(1+nth_prime(n))%nth_prime(k) for k in range(1,n+1)] for n in range(1,16)]) # G. C. Greubel, Apr 10 2024

Extensions

Corrected by D. S. McNeil, Dec 02 2010

A175620 Triangle read by rows: T(n,k) = 2^(prime(n) - k - 1) mod n, 1 <= k <= n.

Original entry on oeis.org

0, 0, 1, 2, 1, 2, 0, 0, 0, 0, 2, 1, 3, 4, 2, 2, 4, 2, 4, 2, 4, 1, 4, 2, 1, 4, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 8, 4, 2, 1, 5, 7, 8, 4, 2, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 6, 3, 7, 9, 10, 5, 8, 4, 2, 1, 6, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 2, 1, 7, 10, 5, 9, 11, 12, 6, 3, 8
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Dec 12 2010

Keywords

Examples

			Triangle begins:
  0;
  0, 1;
  2, 1, 2;
  0, 0, 0, 0;
  2, 1, 3, 4, 2;
  2, 4, 2, 4, 2, 4;

Links

Crossrefs

Cf. A000079, A173655, A177226.

Programs

  • Magma
    [Modexp(2,NthPrime(n)-k-1,n): k in [1..n], n in [1..15]]; // G. C. Greubel, Apr 12 2024
  • Maple
    A175620 := proc(n,k) modp(2^(ithprime(n)-k-1) ,n) ; end proc: # R. J. Mathar, Dec 14 2010
  • Mathematica
    Flatten[Table[PowerMod[2,Prime[n]-k-1,n],{n,20},{k,n}]] (* Harvey P. Dale, Dec 10 2012 *)
  • SageMath
    flatten([[pow(2,nth_prime(n)-k-1,n) for k in range(1,n+1)] for n in range(1,16)]) # G. C. Greubel, Apr 12 2024

A174497 Triangle read by rows: T(n,k) = prime(n) mod (prime(n+1) - prime(k)) for 0 < k < n+1.

Original entry on oeis.org

0, 0, 1, 0, 1, 1, 7, 7, 1, 3, 0, 1, 3, 5, 1, 13, 13, 1, 3, 1, 1, 0, 1, 3, 5, 1, 5, 1, 19, 19, 1, 3, 7, 9, 1, 3, 23, 23, 23, 1, 5, 7, 11, 3, 5, 0, 1, 3, 5, 9, 11, 1, 5, 5, 1, 31, 31, 31, 1, 5, 7, 11, 13, 3, 7, 1, 37, 37, 1, 3, 7, 9, 13, 15, 1, 1, 7, 1, 0, 1, 3, 5, 9, 11, 15, 17, 1, 13, 5, 5, 1
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 28 2010

Keywords

Examples

			Triangle begins as:
   0;
   0,  1;
   0,  1, 1;
   7,  7, 1, 3;
   0,  1, 3, 5, 1;
  13, 13, 1, 3, 1, 1;
   0,  0, 1, 0, 1, 1, 7;
   7,  1, 3, 0, 1, 3, 5, 1;
  13, 13, 1, 3, 1, 1, 0, 1, 3;

Links

Crossrefs

Cf. A000040, A086800, A177226.

Programs

  • Magma
    [NthPrime(n) mod (NthPrime(n+1) - NthPrime(k)): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 10 2024
  • Mathematica
    Table[Mod[Prime[n], Prime[n+1]-Prime[k]], {n,12}, {k,n}]//Flatten (* G. C. Greubel, Apr 10 2024 *)
  • PARI
    T(n, k) = prime(n) % (prime(n+1)-prime(k));
tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n, k), ", ")); print); \\ Michel Marcus, Aug 08 2017
  • Sage
    A174497 = flatten([[nth_prime(n) % (nth_prime(n+1)-nth_prime(k)) for k in range(1,n+1)] for n in range(1, 20)]) # D. S. McNeil, Nov 30 2010

A177806 Triangle read by rows: T(n,k) = prime(k)^(n-1) mod prime(n), 1 <= k <= n.

Original entry on oeis.org

1, 2, 0, 4, 4, 0, 1, 6, 6, 0, 5, 4, 9, 3, 0, 6, 9, 5, 11, 7, 0, 13, 15, 2, 9, 8, 16, 0, 14, 2, 16, 7, 11, 10, 5, 0, 3, 6, 16, 12, 8, 2, 18, 9, 0, 19, 21, 4, 20, 2, 5, 17, 11, 7, 0, 1, 25, 5, 25, 5, 5, 25, 25, 1, 1, 0, 13, 28, 2, 12, 27, 15, 32, 20, 29, 23, 6, 0, 37, 40, 16, 31, 23, 4, 23, 31, 37, 25, 18, 16, 0
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Dec 12 2010

Keywords

Comments

First column is A175036.

Examples

			Triangle begins:
  1;
  2, 0;
  4, 4, 0;
  1, 6, 6, 0;
  5, 4, 9, 3, 0;

Crossrefs

Cf. A000079, A177226.

Programs

  • Maple
    A177806 := proc(n,k) modp((ithprime(k))^(n-1), ithprime(n)) ; end proc:
seq(seq(A177806(n,k),k=1..n),n=1..15) ;
  • Mathematica
    Table[PowerMod[Prime[Range[n]], n-1, Prime[n]], {n, 15}] (* Paolo Xausa, Jun 29 2024 *)

A175623 Triangle read by rows: T(n,k) = prime(k)^(n-1) mod n, 1<=k<=n.

Original entry on oeis.org

0, 0, 1, 1, 0, 1, 0, 3, 1, 3, 1, 1, 0, 1, 1, 2, 3, 5, 1, 5, 1, 1, 1, 1, 0, 1, 1, 1, 0, 3, 5, 7, 3, 5, 1, 3, 4, 0, 7, 4, 4, 7, 1, 1, 7, 2, 3, 5, 7, 1, 3, 7, 9, 3, 9, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 8, 3, 5, 7, 11, 1, 5, 7, 11, 5, 7, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Dec 12 2010

Keywords

Examples

			Triangle begins:
  0;
  0, 1;
  1, 0, 1;
  0, 3, 1, 3;
  1, 1, 0, 1, 1;

Links

Crossrefs

Cf. A000079, A177226, A177806.

Programs

  • Magma
    [Modexp(NthPrime(k), n-1, n): k in [1..n], n in [1..15]]; // G. C. Greubel, Apr 12 2024
  • Mathematica
    T[n_, k_] := Mod[ Prime[k]^(n - 1), n]; Table[ T[n, k], {n, 13}, {k, n}] // Flatten
Flatten[Table[PowerMod[Prime[k],n-1,n],{n,20},{k,n}]] (* Harvey P. Dale, Oct 13 2015 *)
  • SageMath
    flatten([[pow(nth_prime(k),n-1,n) for k in range(1,n+1)] for n in range(1,16)]) # G. C. Greubel, Apr 12 2024

A166865 Triangle read by rows: R(n,k)=prime(k)^(prime(n)-2) mod n, 1<=k<=n.

Original entry on oeis.org

0, 0, 1, 2, 0, 2, 0, 3, 1, 3, 2, 3, 0, 2, 1, 2, 3, 5, 1, 5, 1, 1, 6, 6, 0, 1, 6, 6, 0, 3, 5, 7, 3, 5, 1, 3, 8, 0, 8, 1, 8, 1, 8, 1, 8, 8, 7, 5, 3, 1, 7, 3, 9, 7, 9, 6, 4, 9, 8, 0, 6, 2, 7, 1, 8, 5, 8, 3, 5, 7, 11, 1, 5, 7, 11, 5, 7, 1
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Dec 16 2010

Keywords

Comments

Row sums: 0, 1, 4, 7, 8, 17, 26, 27, 43, 59, 56, 71, …, .

Examples

			Triangle begins:
0,
0, 1,
2, 0, 2,
0, 3, 1, 3,
2, 3, 0, 2, 1,
2, 3, 5, 1, 5, 1,

Crossrefs

Cf. A000079, A177226.

Programs

  • Mathematica
    t[n_, k_] := Mod[Prime@ k^(Prime@ n - 2), n]; Table[ t[n, k], {n, 12}, {k, n}] // Flatten
Showing 1-7 of 7 results.

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

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