A308268 - OEIS

%I #24 Jul 15 2024 06:03:37

%S 10,12,15,16,21,25,27,35,39,55,57,65,75,77,85,93,95,115,119,129,143,

%T 145,155,183,185,187,189,196,203,205,215,219,231,235,245,253,265,287,

%U 295,297,299,305,309,323,325,327,335,341,351,355,357,363,365,375,377,385,395,405,407,413,415,417,429

%N Numbers k such that 1 + A045763(k) is prime.

%C Numbers k such that k - phi(k) - tau(k) (i.e., k - A000010(k) - A000005(k)) is prime.

%C For distinct primes p and q, p*q is in the sequence if and only if p+q-5 is prime. In particular, 5*p is in the sequence for any prime p.

%C For prime p, 4*p^2 is in the sequence if and only if p is in A308269.

%H Robert Israel, <a href="/A308268/b308268.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 15 is in the sequence because 1 + A045763(15) = 15 - phi(15) - tau(15) = 15 - 8 - 4 = 3 is prime.

%p select(t -> isprime(t - numtheory:-phi(t) - numtheory:-tau(t)), [$1..1000]);

%Y Cf. A000005, A000010, A045763, A308269.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, May 17 2019