A192638 Numbers n such that 4n + 3 and 16n + 15 are prime.

1, 2, 4, 7, 11, 14, 16, 26, 37, 44, 56, 67, 76, 82, 89, 91, 109, 116, 121, 124, 142, 146, 149, 161, 172, 179, 209, 226, 247, 254, 257, 259, 296, 314, 319, 322, 326, 329, 341, 356, 361, 362, 364, 377, 391, 392, 436, 439, 446, 452, 467, 482, 494, 496

Offset

1,2

Comments

Infinite under Dickson's conjecture. [Charles R Greathouse IV, Jul 06 2011]

No n can be a multiple of 3. If it is 1 mod 3, it cannot end in 3 or 8. If it is 2 mod 3, it cannot end in 1 or 6. One can see the potential of iterative chains producing primes.

Links

Table of n, a(n) for n=1..54.

Example

For n=37, 4*37+3=151 and 16*37+15=607.

Mathematica

Select[Range[500], PrimeQ[4# + 3] && PrimeQ[16# + 15] &] (* Alonso del Arte, Jul 06 2011 *)

Prog

(PARI) for(n=1, 1e3, if(isprime(4*n+3)&&isprime(16*n+15), print1(n", "))) \\ Charles R Greathouse IV, Jul 06 2011

Crossrefs

Cf. A002145.

Sequence in context: A086795 A064690 A138766 * A211372 A054850 A225154

Adjacent sequences: A192635 A192636 A192637 * A192639 A192640 A192641

Keyword

nonn

Author

J. M. Bergot, Jul 06 2011

Status

approved