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

1,2

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.

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

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A001122, A005098, A005124.

Sequence in context: A212979 A114961 A219045 * A178508 A123834 A064629

Adjacent sequences: A199424 A199425 A199426 * A199428 A199429 A199430

Keyword

nonn

Author

Martin Renner, Nov 06 2011

Status

approved