A036261 Triangle of numbers arising from Gilbreath's conjecture: successive absolute differences of primes (read by antidiagonals upwards, omitting the initial row of primes).

1, 1, 2, 1, 0, 2, 1, 2, 2, 4, 1, 2, 0, 2, 2, 1, 2, 0, 0, 2, 4, 1, 2, 0, 0, 0, 2, 2, 1, 2, 0, 0, 0, 0, 2, 4, 1, 2, 0, 0, 0, 0, 0, 2, 6, 1, 0, 2, 2, 2, 2, 2, 2, 4, 2, 1, 0, 0, 2, 0, 2, 0, 2, 0, 4, 6, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 4, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 4

Offset

1,3

Comments

A variant of A036262, which is the main entry for this array.

References

R. K. Guy, Unsolved Problems Number Theory, A10.

C. A. Pickover, The Math Book, Sterling, NY, 2009; see p. 410.

Links

T. D. Noe, Rows n=1..100 of triangle, flattened

A. M. Odlyzko, Iterated absolute values of differences of consecutive primes, Math. Comp. 61 (1993), 373-380.

Wikipedia, Gilbreath's conjecture.

Index entries for sequences related to Gilbreath conjecture and transform

Example

Table begins (conjecture is leading term is always 1):
  2 3 5 7 11 13 17 19 23 ...
  1 2 2 4  2  4  2  4 ...
  1 0 2 2  2  2  2 ...
  1 2 0 0  0, 0 ...
  1 2 0 0  0 ...
  1 2 0 0 ...
  ...

Mathematica

max = 15; triangle = Rest[ NestList[ Abs[ Differences[#] ]& , Prime[ Range[max] ], max] ]; Flatten[ Table[ triangle[[n-k+1, k]], {n, 1, max-1}, {k, 1, n}]] (* Jean-François Alcover, Jan 23 2012 *)

Crossrefs

Cf A036262.

Sequence in context: A035443 A180430 A246369 * A140575 A091917 A025657

Adjacent sequences: A036258 A036259 A036260 * A036262 A036263 A036264

Keyword

tabl,easy,nice,nonn

Author

N. J. A. Sloane

Extensions

More terms from Naohiro Nomoto, May 22 2001

Status

approved