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 1-5 of 5 results.

A177226 Triangle read by rows: T(n, k) = 2^(prime(n) - prime(k)) mod prime(n), 1 <= k <= n.

Original entry on oeis.org

1, 2, 1, 3, 4, 1, 4, 2, 4, 1, 6, 3, 9, 5, 1, 7, 10, 9, 12, 4, 1, 9, 13, 16, 4, 13, 16, 1, 10, 5, 6, 11, 9, 7, 4, 1, 12, 6, 13, 9, 2, 12, 18, 16, 1, 15, 22, 20, 5, 13, 25, 7, 9, 6, 1, 16, 8, 2, 16, 1, 8, 16, 4, 8, 4, 1, 19, 28, 7, 11, 3, 10, 33, 36, 30, 34, 27, 1, 21, 31, 18, 25, 40, 10, 16, 4, 31, 37, 40, 16, 1
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Dec 10 2010

Keywords

Examples

			Triangle begins:
   1;
   2,  1;
   3,  4,  1;
   4,  2,  4,  1;
   6,  3,  9,  5,  1;
   7, 10,  9, 12,  4,  1;
   9, 13, 16,  4, 13, 16,  1;
  10,  5,  6, 11,  9,  7,  4,  1;
  12,  6, 13,  9,  2, 12, 18, 16,  1;

Links

Crossrefs

Cf. A000079, A111333, A173655, A174497, A174947, A174996, A292411.

Programs

  • Magma
    A177226:= func< n,k | Modexp(2, NthPrime(n) - NthPrime(k), NthPrime(n)) >;
[A177226(n,k): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 09 2024
  • Mathematica
    Flatten[Table[PowerMod[2,Prime[n]-Prime[k],Prime[n]],{n,20},{k,n}]] (* Harvey P. Dale, May 10 2014 *)
  • SageMath
    def A177226(n,k): return pow(2, nth_prime(n) - nth_prime(k), nth_prime(n))
flatten([[A177226(n,k) for k in range(1,n+1)] for n in range(1,13)]) # G. C. Greubel, Apr 09 2024

Formula

From G. C. Greubel, Apr 09 2024: (Start)
T(n, 1) = A111333(n).
T(n, 2) = A292411(n). (End)

Extensions

Corrected by D. S. McNeil, Dec 10 2010

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

A173662 Triangle read by rows: T(n,k) = semiprime(n) mod semiprime(k), 1 <= k <= n.

Original entry on oeis.org

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

Views

Author

Juri-Stepan Gerasimov, Nov 28 2010

Keywords

Comments

Row sums are 0, 2, 4, 7, 13, 18, 28, ...

Examples

			Triangle begins:
  0,
  2,0;
  1,3,0;
  2,4,1,0;
  2,2,5,4,0;
  3,3,6,5,1,0;
  1,3,3,1,7,6,0;
  2,4,4,2,8,7,1,0;

Crossrefs

Cf. A001358, A173655.

Programs

  • Mathematica
    SemiprimeQ[n_Integer] := If[Abs[n]<2, False, (2==Plus@@Transpose[FactorInteger[Abs[n]]][[2]])]; sp = Select[Range[100], SemiprimeQ]; Flatten[Table[Mod[sp[[n]], sp[[Range[n]]]], {n,Length[sp]}]]

Extensions

46th term corrected by D. S. McNeil, Nov 24 2010
Showing 1-5 of 5 results.

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