A199427 Numbers n such that 4n+1 and 8n+3 are prime.

1, 7, 10, 13, 22, 28, 43, 58, 70, 73, 127, 148, 160, 163, 190, 202, 238, 253, 262, 307, 322, 352, 370, 400, 433, 472, 475, 493, 517, 532, 535, 568, 598, 637, 673, 685, 688, 742, 832, 847, 853, 862, 898, 940, 955, 1018, 1087, 1093, 1102, 1120, 1183, 1198, 1270

Offset: 1

Author

Martin Renner, Nov 06 2011

Keywords

• nonn

Comments

According to Beiler: the integer 2 is a primitive root of all primes of the form 8n+3 provided 4n+1 is a prime.

Examples

			For n = 1, both 11 and 5 are primes, hence 2 is a primitive root of 11.
		

References

• Albert H. Beiler: Recreations in the theory of numbers. New York: Dover, (2nd ed.) 1966, p. 102, nr. 4.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001122, A005098, A005124.

Programs

Mathematica

Select[Range[1270], PrimeQ[4*# + 1] && PrimeQ[8*# + 3] &] (* T. D. Noe, Nov 07 2011 *)

Formula

a(n) = intersection(A005098, A005124).