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
Examples
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 ... ...
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
Crossrefs
Cf A036262.
Programs
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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 *)
Extensions
More terms from Naohiro Nomoto, May 22 2001
Comments