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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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.) LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE 4 is a term since f(4) is a local maximum: f(3)=2, f(4)=4, f(5)=2. 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, (f[ # ]-f[ #-1])(f[ # ]-f[ #+1])>0&] PROG (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)) || ((x

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Last modified January 16 21:00 EST 2021. Contains 340213 sequences. (Running on oeis4.)