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A192638 Numbers n such that 4n + 3 and 16n + 15 are prime. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 20 05:01 EDT 2019. Contains 324229 sequences. (Running on oeis4.)