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

Author

Felix Fröhlich, Jan 07 2018

Keywords

• nonn

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.

Examples

			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.
		

Links

• Wikipedia, Sexy prime

Crossrefs

Cf. A023201, A023271, A046118, A140555.

Programs

Mathematica

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

PARI

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