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A297847
Sexiness of p = prime(n): number of iterations of the function f(x) = x + 6 that leave p prime.
0
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.
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
KEYWORD
nonn
AUTHOR
Felix Fröhlich, Jan 07 2018
STATUS
approved