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A110581 Primes p such that 2p-1 is prime, but 4p-3 is not prime. 3


%S 3,7,31,37,97,139,157,199,211,229,271,307,337,367,379,547,577,601,607,

%T 661,691,727,811,877,937,967,997,1009,1171,1237,1297,1399,1429,1459,

%U 1609,1627,1657,1759,1867,2011,2029,2137,2221,2281,2467,2539,2551,2557

%N Primes p such that 2p-1 is prime, but 4p-3 is not prime.

%C A subsequence of A005382, primes p such that 2p-1 is also prime. Note that for all n, 2a(n)-1 is not in this sequence.

%H T. D. Noe, <a href="/A110581/b110581.txt">Table of n, a(n) for n=1..1000</a>

%H Jeffery J. Holt, <a href="http://dx.doi.org/10.1090/S0025-5718-03-01509-6">The minimal number of solutions to phi(n)=phi(n+k)</a>, Math. Comp., 72 (2003), 2059-2061.

%t Select[Prime[Range[2, 1000]], PrimeQ[2#-1] && !PrimeQ[4#-3]&]

%o (MAGMA) [p: p in PrimesUpTo(2600) | IsPrime(2*p-1) and not IsPrime(4*p-3)]; // _Vincenzo Librandi_, Apr 14 2013

%K nonn,easy

%O 1,1

%A _T. D. Noe_, Jul 28 2005

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Last modified April 7 15:03 EDT 2020. Contains 333305 sequences. (Running on oeis4.)