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A217199 Odd primes p such that 2p-1 is prime and no p is equal to 2q-1 with q in the sequence. 3

%I

%S 3,7,19,31,79,97,139,199,211,229,271,307,331,337,367,379,439,499,547,

%T 577,601,607,619,691,727,811,829,937,967,1009,1069,1171,1279,1297,

%U 1399,1429,1459,1531,1609,1627,1759,1867,2011,2029,2089,2131,2179,2221,2281

%N Odd primes p such that 2p-1 is prime and no p is equal to 2q-1 with q in the sequence.

%C At each step, the smallest possible p is chosen.

%C These are the primes described in lemma 2 of the paper by Holt. - _T. D. Noe_, Sep 28 2012

%H Michel Marcus, <a href="/A217199/b217199.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.

%H A. Schinzel and Andrzej Wakulicz, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa4/aa431.pdf">Sur l'équation phi(x+k)=phi(x), I.</a>, Acta Arith. 4 (1958), 181-184.

%t t = {}; p = 2; Do[p = NextPrime[p]; If[PrimeQ[2*p - 1] && ! MemberQ[2*t - 1, p], AppendTo[t, p]], {PrimePi[2281]}]; t

%o (PARI) intab(val, tab) = {for (ii=1, length(tab),if (tab[ii] == val, return (1);););return(0);} prseq(n) = {tab = [];for (i=1, n, len = length(tab);if (len == 0, p = 3, p = nextprime(tab[len]+1));while (! isprime(2*p-1) || intab((p+1)/2, tab) , p = nextprime(p+1);); tab = concat(tab, p); print1(p, ", "););}

%Y Cf. A110581, A217198.

%K nonn

%O 1,1

%A _Michel Marcus_, Sep 27 2012

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Last modified February 22 18:24 EST 2020. Contains 332148 sequences. (Running on oeis4.)