A297847 - OEIS

%I #10 Jan 22 2018 08:13:35

%S 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,

%T 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,

%U 2,0,1,0,2,1,0,1,0,0,0,0,0,0,0,1,0,1,0

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

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

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

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

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

%C 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.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Sexy_prime">Sexy prime</a>

%e 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.

%t Array[-2 + Length@ NestWhileList[# + 6 &, Prime@ #, PrimeQ] &, 105] (* _Michael De Vlieger_, Jan 11 2018 *)

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

%Y Cf. A023201, A023271, A046118, A140555.

%K nonn

%O 1,3

%A _Felix Fröhlich_, Jan 07 2018