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A199427 Numbers n such that 4n+1 and 8n+3 are prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 25 12:00 EST 2021. Contains 341606 sequences. (Running on oeis4.)