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%I #30 Oct 31 2023 15:58:06
%S 3,11,23,29,83,89,131,191,251,431,443,491,509,683,743,809,911,1031,
%T 1049,1103,1223,1229,1289,1409,1451,1511,1583,1811,1889,1931,2003,
%U 2063,2069,2129,2351,2543,2549,2903,2963,2969,3023,3329,3389,3449,3491,3623,3803
%N Primes p == 3, 9, 11 (mod 20) such that 2p+1 is also prime.
%C a(n) = (A000353(n)-1)/2. - _Reinhard Zumkeller_, Feb 10 2009
%H Reinhard Zumkeller, <a href="/A000355/b000355.txt">Table of n, a(n) for n = 1..1000</a>
%H Robert A. J. Matthews, <a href="https://www.researchgate.net/publication/266728416_Maximally_periodic_reciprocals">Maximally periodic reciprocals</a>, Bull. Institute of Mathematics and Its Applications, vol. 28, p. 147-148, 1992.
%p q:= p-> irem(p, 20) in {3, 9, 11} and andmap(isprime, [p,2*p+1]):
%p select(q, [$1..10000])[]; # _Alois P. Heinz_, Oct 31 2023
%t Select[Prime[Range[1000]], MatchQ[Mod[#, 20], 3|9|11] && PrimeQ[2#+1]&] (* _Jean-François Alcover_, Feb 07 2016 *)
%o (PARI) is(n)=my(k=n%20); (k==3||k==9||k==11) && isprime(2*n+1) && isprime(n) \\ _Charles R Greathouse IV_, Nov 20 2014
%Y Subset of A005384.
%Y Cf. A000353.
%K nonn,easy
%O 1,1
%A _Robert A. J. Matthews_
%E More terms from _Reinhard Zumkeller_, Feb 10 2009
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