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

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