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

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

1,1

Comments

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

Links

Table of n, a(n) for n=1..72.

Wikipedia, Gilbreath's conjecture

Example

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 ...              .

Prog

(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

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.

Sequence in context: A331179 A026100 A059127 * A105609 A268361 A330569

Adjacent sequences: A319491 A319492 A319493 * A319495 A319496 A319497

Keyword

nonn,tabl

Author

Tristan Cam, Sep 20 2018

Status

approved