A066485 Numbers n such that f(n) is a strict local extremum for the prime gaps function f(n) = prime(n+1)-prime(n), where prime(n) denotes the n-th prime; i.e., either f(n)>f(n-1) and f(n)>f(n+1) or f(n)

4, 5, 6, 7, 9, 10, 11, 13, 17, 18, 20, 21, 22, 24, 26, 27, 28, 30, 31, 32, 33, 34, 35, 38, 41, 42, 43, 44, 45, 49, 51, 52, 53, 57, 58, 60, 62, 64, 66, 67, 68, 69, 72, 75, 77, 78, 80, 81, 82, 83, 84, 85, 87, 89, 91, 93, 94, 95, 97, 98, 99, 100, 101, 104, 106, 109, 113, 114

Offset: 1

Author

Joseph L. Pe, Jan 02 2002

Keywords

• nonn

Comments

Call a finite subsequence of consecutive terms of a(n) a "zigzag" if it consists of consecutive integers; for example, 30, 31, 32, 33, 34, 35 is a zigzag. Are there zigzags of arbitrary length? (Cf. A066918.)

Examples

			4 is a term since f(4) is a local maximum: f(3)=2, f(4)=4, f(5)=2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A066918, A001223.

Cf. A198696 (local maxima), A196174 (local minima).

Programs

Maple

Primes:= select(isprime,[2,seq(2*i+1,i=1..10^3)]):
G:= Primes[2..-1] - Primes[1..-2]:
select(n -> G[n] > max(G[n-1],G[n+1]) or G[n] < min(G[n-1],G[n+1]), [$2..nops(G)-1]):
# Robert Israel, Sep 20 2015

Mathematica

f[n_] := Prime[n+1]-Prime[n]; Select[Range[200], (f[ # ]-f[ #-1])(f[ # ]-f[ #+1])>0&]

PARI

f(n) = prime(n+1)-prime(n);
isok(n) = if (n>2, my(x=f(n), y=f(n-1), z=f(n+1)); ((x>y) && (x>z)) || ((xMichel Marcus, Mar 26 2020

Extensions

Edited by Dean Hickerson, Jun 26 2002