|
%I #31 Sep 25 2023 19:19:14
%S 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,
%T 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,
%U 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
%N Triangle of numbers arising from Gilbreath's conjecture: successive absolute differences of primes (read by antidiagonals upwards, omitting the initial row of primes).
%C A variant of A036262, which is the main entry for this array.
%D R. K. Guy, Unsolved Problems Number Theory, A10.
%D C. A. Pickover, The Math Book, Sterling, NY, 2009; see p. 410.
%H T. D. Noe, <a href="/A036261/b036261.txt">Rows n=1..100 of triangle, flattened</a>
%H A. M. Odlyzko, <a href="http://dx.doi.org/10.1090/S0025-5718-1993-1182247-7">Iterated absolute values of differences of consecutive primes</a>, Math. Comp. 61 (1993), 373-380.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Gilbreath%27s_conjecture">Gilbreath's conjecture</a>.
%H <a href="/index/Ge#Gilbreath">Index entries for sequences related to Gilbreath conjecture and transform</a>
%e Table begins (conjecture is leading term is always 1):
%e 2 3 5 7 11 13 17 19 23 ...
%e 1 2 2 4 2 4 2 4 ...
%e 1 0 2 2 2 2 2 ...
%e 1 2 0 0 0, 0 ...
%e 1 2 0 0 0 ...
%e 1 2 0 0 ...
%e ...
%t 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 *)
%Y Cf A036262.
%K tabl,easy,nice,nonn
%O 1,3
%A _N. J. A. Sloane_
%E More terms from _Naohiro Nomoto_, May 22 2001
|
