A308268 Numbers k such that 1 + A045763(k) is prime.

10, 12, 15, 16, 21, 25, 27, 35, 39, 55, 57, 65, 75, 77, 85, 93, 95, 115, 119, 129, 143, 145, 155, 183, 185, 187, 189, 196, 203, 205, 215, 219, 231, 235, 245, 253, 265, 287, 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

Offset: 1

Author

J. M. Bergot and Robert Israel, May 17 2019

Keywords

• nonn

Comments

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

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.

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

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000010, A045763, A308269.

Programs

Maple

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