OFFSET
1,1
COMMENTS
Esparza and Gehring (2018) proved that assuming a generalized Hardy-Littlewood conjecture the number of terms not exceeding x is asymptotically (c/2) * x/log(x)^3, where c = A343480 = 5.716497...
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Carlos Esparza and Lukas Gehring, Estimating the density of a set of primes with applications to group theory, arXiv:1810.08679 [math.NT], 2018.
EXAMPLE
29 is a term since it is prime, 29 = 3*9 + 2, 29-1 = 28 = 2^2 * 7 has only one distinct odd prime divisor (7) and 29+1 = 30 = 2*3*5 has only one distinct prime divisor (5) larger than 3.
101 is a term since it is prime, 101 = 3*33 + 2, 101-1 = 100 = 2^2 * 5^2 has only one distinct odd prime divisor (5) and 101+1 = 102 = 2^2*3*17 has only one distinct prime divisor (17) larger than 3.
MATHEMATICA
q[n_] := Mod[n, 3] == 2 && PrimeQ[n] && PrimeNu[(n + 1)/2^IntegerExponent[n + 1, 2]/3^IntegerExponent[n + 1, 3]] == 1 && PrimeNu[(n - 1)/2^IntegerExponent[n - 1, 2]] == 1; Select[Range[1500], q]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Apr 16 2021
STATUS
approved