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.)

13, 17, 9, 4, 41, 30, 293, 166, 484, 796, 134, 12209, 1646, 467, 4673, 763, 1573, 7279, 37989, 153772, 102051, 377198, 593191, 41552, 677313, 473395, 557448, 5536093, 1643927, 22986338, 1877982, 14184432, 14828672, 23278807, 45383008, 82020263

Offset: 1

Author

Joseph L. Pe, Jan 23 2002

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A066485.

Programs

Mathematica

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]]

Extensions

Edited by Dean Hickerson, Jun 26 2002