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 A066918 a(n) = least natural number k such that f(k) begins a maximal zigzag of length n in the prime gaps function f(x) = p(x+1)-p(x), where p(x) denotes the x-th prime. (Cf. A066485.) 2

%I

%S 13,17,9,4,41,30,293,166,484,796,134,12209,1646,467,4673,763,1573,

%T 7279,37989,153772,102051,377198,593191,41552,677313,473395,557448,

%U 5536093,1643927,22986338,1877982,14184432,14828672,23278807,45383008,82020263

%N a(n) = least natural number k such that f(k) begins a maximal zigzag of length n in the prime gaps function f(x) = p(x+1)-p(x), where p(x) denotes the x-th prime. (Cf. A066485.)

%C A zigzag of a function f(n) is a run of consecutive strict local extrema.

%e f(11),f(12),...,f(15) are: 6, 4, 2, 4, 6. Note that a zigzag of length 1 occurs at f(13)=2. This is a maximal zigzag, since neither f(12)=4 nor f(14)=4 are local extrema of f. Also, a maximal zigzag of length 1 first occurs at f(13). Therefore a(1) = 13.

%t f[n_] := Prime[n+1]-Prime[n]; e[n_] := (f[n]-f[n-1])(f[n]-f[n+1])>0; For[n=1, n<100, n++, a[n]=0]; For[k=4; l=0, True, k++, If[e[k], l++, If[a[l]===0, Print["a(", l, ")=", a[l]=k-l]]; l=0]]

%Y Cf. A066485.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Jan 23 2002

%E Edited by _Dean Hickerson_, Jun 26 2002

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Last modified March 25 15:48 EDT 2023. Contains 361528 sequences. (Running on oeis4.)