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%I #6 Nov 27 2022 11:07:21
%S 0,0,1,2,3,3,3,3,1,8,7,5,7,9,5,8,5,9,10,10,8,9,10,11,10,10,17,12,17,
%T 12,13,8,20,22,18,17,14,25,20,24,24,22,21,15,19,25,25,25,24,24,21,23,
%U 27,24,23,29,32,19,26,36,34,34,31,27,35,38,35,37,25,37
%N a(n) is the number of zeros among the first n terms of row n of the Gilbreath array shown in A036262.
%C Conjecture: If = (a(n)/n), then (lim inf S) > 2/5 and (lim sup S) < 3/5.
%e Corner of Gilbreath array:
%e 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101
%e 1 2 2 4 2 4 2 4 6 2 6 4 2 4 6 6 2 6 4 2 6 4 6 8 4 2
%e 1 0 2 2 2 2 2 2 4 4 2 2 2 2 0 4 4 2 2 4 2 2 2 4 2 2
%e 1 2 0 0 0 0 0 2 0 2 0 0 0 2 4 0 2 0 2 2 0 0 2 2 0 0
%e 1 2 0 0 0 0 2 2 2 2 0 0 2 2 4 2 2 2 0 2 0 2 0 2 0 0
%e 1 2 0 0 0 2 0 0 0 2 0 2 0 2 2 0 0 2 2 2 2 2 2 2 0 8
%e 1 2 0 0 2 2 0 0 2 2 2 2 2 0 2 0 2 0 0 0 0 0 0 2 8 8
%e 1 2 0 2 0 2 0 2 0 0 0 0 2 2 2 2 2 0 0 0 0 0 2 6 0 8
%e 1 2 2 2 2 2 2 2 0 0 0 2 0 0 0 0 2 0 0 0 0 2 4 6 8 6
%e 1 0 0 0 0 0 0 2 0 0 2 2 0 0 0 2 2 0 0 0 2 2 2 2 2 4
%t z = 2000; t = Prime[Range[z]]; r[1] = t; r[2] = Abs[Differences[t]];
%t r[n_] := r[n] = Abs[Differences[r[n - 1]]];
%t Table[Count[Take[r[n], n], 0], {n, 1, z/2}]
%Y Cf. A000040, A036262, A358616.
%K nonn
%O 1,4
%A _Clark Kimberling_, Nov 23 2022
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