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A000353 Primes p == 7, 19, 23 (mod 40) such that (p-1)/2 is also prime.

%I A000353 #36 Jan 20 2024 03:53:00
%S A000353 7,23,47,59,167,179,263,383,503,863,887,983,1019,1367,1487,1619,1823,
%T A000353 2063,2099,2207,2447,2459,2579,2819,2903,3023,3167,3623,3779,3863,
%U A000353 4007,4127,4139,4259,4703,5087,5099,5807,5927,5939,6047,6659,6779,6899,6983,7247
%N A000353 Primes p == 7, 19, 23 (mod 40) such that (p-1)/2 is also prime.
%C A000353 The decimal expansion of 1/a(n) will produce a stream of a(n)-1 pseudo-random digits. - _Reinhard Zumkeller_, Feb 10 2009
%C A000353 The condition in the name is sufficient for primes p such that the decimal expansion of 1/p recurs after p-1 digits, which is the maximum-possible cycle length. - _Robert A. J. Matthews_, Oct 31 2023
%H A000353 Reinhard Zumkeller, <a href="/A000353/b000353.txt">Table of n, a(n) for n = 1..1000</a>
%H A000353 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.
%H A000353 Wikipedia, <a href="http://en.wikipedia.org/wiki/Sophie_Germain_prime">Sophie Germain prime</a>
%H A000353 <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n.</a>
%F A000353 a(n) = 2*A000355(n)+1. - _Reinhard Zumkeller_, Feb 10 2009
%p A000353 q:= p-> irem(p, 40) in {7, 19, 23} and andmap(isprime, [p, (p-1)/2]):
%p A000353 select(q, [$1..10000])[];  # _Alois P. Heinz_, Oct 31 2023
%t A000353 Select[Prime[Range[1000]], MatchQ[Mod[#, 40], 7|19|23] && PrimeQ[(#-1)/2]&] (* _Jean-François Alcover_, Feb 07 2016 *)
%o A000353 (PARI) is(n)=my(k=n%40); (k==7||k==19||k==23) && isprime(n\2) && isprime(n) \\ _Charles R Greathouse IV_, Nov 20 2014
%Y A000353 Subset of A005385.
%Y A000353 Subsequence of A001913, A006883.
%K A000353 nonn
%O A000353 1,1
%A A000353 _Robert A. J. Matthews_
%E A000353 More terms from _Reinhard Zumkeller_, Feb 10 2009