

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 nth prime; i.e., either f(n)>f(n1) and f(n)>f(n+1) or f(n)<f(n1) and f(n)<f(n+1).


4



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
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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[n1], G[n+1]) or G[n] < min(G[n1], 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&]


PROG

(PARI) f(n) = prime(n+1)prime(n);
isok(n) = if (n>2, my(x=f(n), y=f(n1), z=f(n+1)); ((x>y) && (x>z))  ((x<y) && (x<z))); \\ Michel Marcus, Mar 26 2020


CROSSREFS

Cf. A066918.
Cf. A198696 (local maxima), A196174 (local minima).
Sequence in context: A201739 A329782 A218044 * A079445 A120173 A075862
Adjacent sequences: A066482 A066483 A066484 * A066486 A066487 A066488


KEYWORD

nonn


AUTHOR

Joseph L. Pe, Jan 02 2002


EXTENSIONS

Edited by Dean Hickerson, Jun 26 2002


STATUS

approved



