A297847 Sexiness of p = prime(n): number of iterations of the function f(x) = x + 6 that leave p prime.

0, 0, 4, 2, 3, 1, 2, 0, 1, 0, 2, 1, 3, 0, 2, 1, 0, 3, 2, 0, 1, 0, 1, 0, 2, 2, 1, 1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 2, 1, 0, 0, 1, 1, 0, 0, 0, 1, 2, 0, 1, 0, 0, 3, 2, 1, 0, 2, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 2, 0, 1, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0

Offset

1,3

Comments

a(n) > 0 iff p is a term of A023201.

a(n) = 0 iff p is a term of A140555.

a(n) = 2 iff p is a term of A046118.

a(n) > 2 iff p is a term of A023271.

a(n) < 4 except for n = 3. Proof: The last digits of the numbers in the progression repeat 1, 7, 3, 9, 5, 1, 7, 3, 9, 5, ..., so a(n) is at most 4, which only happens for p = 5, since A007652(n) = 5 only for n = 3.

Links

Table of n, a(n) for n=1..87.

Wikipedia, Sexy prime

Example

For n = 13: prime(13) = 41 and 41 remains prime through exactly 3 iterations of f(x) = x + 6, since 47, 53 and 59 are prime, but 65 is composite, so a(13) = 3.

Mathematica

Array[-2 + Length@ NestWhileList[# + 6 &, Prime@ #, PrimeQ] &, 105] (* Michael De Vlieger, Jan 11 2018 *)

Prog

(PARI) a(n) = my(p=prime(n), x=p, i=0); while(1, x=x+6; if(!ispseudoprime(x), return(i), i++))

Crossrefs

Cf. A023201, A023271, A046118, A140555.

Sequence in context: A266147 A326046 A231169 * A145326 A178915 A222221

Adjacent sequences: A297844 A297845 A297846 * A297848 A297849 A297850

Keyword

nonn

Author

Felix Fröhlich, Jan 07 2018

Status

approved