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 1-3 of 3 results.

A036273 Absolute values of differences of A036272.

Original entry on oeis.org

1, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 4, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 8, 8, 8, 6, 2, 4, 4, 0, 2, 2, 2, 2, 0, 4, 6, 6, 8, 2, 2, 2, 6, 0, 2, 2, 0, 0, 4, 4, 4, 2, 2, 6, 2, 2, 2, 8, 8, 6, 2, 0, 2, 6, 0, 0, 2, 0, 2, 0, 2, 2, 2, 4, 6, 0, 4, 2, 2, 0, 2, 0, 2, 6, 2, 4, 0, 0, 2
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Crossrefs

Cf. A036262, A036263.

Programs

  • Mathematica
    Nest[Abs[Differences[#]]&,Prime[Range[100]],4] (* Harvey P. Dale, Jan 05 2012 *)

A194947 Absolute values of differences of A036274.

Original entry on oeis.org

1, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 8, 8, 0, 2, 2, 2, 2, 4, 2, 2, 0, 0, 2, 2, 2, 2, 2, 4, 6, 0, 4, 2, 4, 2, 2, 2, 4, 4, 0, 2, 2, 4, 0, 4, 0, 6, 6, 2, 2, 2, 0, 2, 2, 6, 2, 0, 0, 0, 0, 2, 0, 2, 0, 4, 2, 2, 2, 2, 0, 0, 0, 2
Offset: 1

Views

Author

Umut Uludag, Jan 02 2013

Keywords

Examples

			a(1) = abs(A036274(1) - A036274(2)); a(2) = abs(A036274(2) - A036274(3)) ...

Crossrefs

Cf. A036274, A036273, A036272, A036263, A001223. These sequences are (absolute, except for A036263) n-th differences of primes (n=5,4,3,2,1).

A319494 Triangle of the consecutive absolute differences between consecutive elements of the previous row, first row being the prime numbers (A000040), read by columns.

Original entry on oeis.org

2, 1, 3, 1, 2, 1, 5, 0, 1, 2, 2, 1, 7, 2, 2, 1, 4, 0, 2, 1, 11, 2, 0, 2, 1, 2, 0, 0, 2, 1, 13, 2, 0, 0, 2, 1, 4, 0, 0, 0, 0, 1, 17, 2, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 0, 1, 19, 2, 0, 2, 2, 0, 0, 1, 4, 0, 2, 0, 0, 0, 0, 1
Offset: 1

Views

Author

Tristan Cam, Sep 20 2018

Keywords

Comments

Gilbreath's conjecture says that the first element of each row except the first row equals 1. - Rémy Sigrist, Nov 15 2018

Examples

			1st column
| 2nd column
| | 3rd column
| | | 4th column
v | v |   ...
  v   v
2   3   5   7  11  13  17  19  23  29  31  37  41  43  47 ...
  1   2   2   4   2   4   2   4   6   2   6   4   2   4 ...
    1   0   2   2   2   2   2   2   4   4   2   2   2 ...
      1   2   0   0   0   0   0   2   0   2   0   0 ...    .
        1   2   0   0   0   0   2   2   2   2   0 ...         .
          1   2   0   0   0   2   0   0   0   2 ...              .
            1   2   0   0   2   2   0   0   2 ...    .
              1   2   0   2   0   2   0   2 ...         .
                1   2   2   2   2   2   2 ...              .
                  1   0   0   0   0   0 ...    .
                    1   0   0   0   0 ...         .
                      1   0   0   0 ...              .
                        1   0   0 ...    .
                          1   0 ...         .
                            1 ...              .

Links

Crossrefs

First row consists of the prime numbers (A000040).
Second row gives the absolute values of differences between consecutive primes (A001223).
Third row gives the absolute values of second differences between primes (A036263 in absolute value).
Fourth row gives the absolute values of differences of absolute values of second differences between primes (A036272).
...
Cf. A036261.

Programs

  • PARI
    T(n, k) = {if (k==n, return (prime(n))); abs(T(n, k+1) - T(n-1, k));}
tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n,k), ", ")); print); \\ Michel Marcus, Oct 28 2018
Showing 1-3 of 3 results.

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

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