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A066388 Numbers n such that n and 2n are both between a pair of twin primes. 9

%I

%S 6,30,660,810,2130,2550,3330,3390,5850,6270,10530,33180,41610,44130,

%T 53550,55440,57330,63840,65100,70380,70980,72270,74100,74760,78780,

%U 80670,81930,87540,93240,102300,115470,124770,133980,136950,156420

%N Numbers n such that n and 2n are both between a pair of twin primes.

%C Also terms of A014574 such that twice the term is also in A014574. Related to a problem of anti-divisors.

%C A117499(a(n)) = 4. - _Reinhard Zumkeller_, Mar 23 2006

%C All a(n)>6 must be a multiple of 30: As for elements of A014574, we must have a(n) = 6k, and k=5m+/-1 would lead to a(n)-/+1 divisible by 5, while k=5m+/-2 would lead to 2a(n)+/-1 divisible by 5, so only k=5m is possible. - _M. F. Hasler_, Nov 27 2010

%H Harry J. Smith, <a href="/A066388/b066388.txt">Table of n, a(n) for n=1,...,1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BitwinChain.html">Bitwin Chain</a>

%e For n=30, 29 and 31 are prime, as are 59 and 61.

%t lst={}; Do[p1=Prime[n]; p2=Prime[n+1]; d=2; If[p2-p1==d, w=p1+1; If[PrimeQ[2*w-1]&&PrimeQ[2*w+1], AppendTo[lst, w]]], {n, 1, 10^4}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 07 2008 *)

%o (PARI) { n=0; forstep (m=2, 10^9, 2, if (isprime(m - 1) && isprime(m + 1) && isprime(2*m - 1) && isprime(2*m + 1), write("b066388.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Feb 13 2010

%Y Cf. A001359, A006512, A012574.

%K nonn

%O 1,1

%A _Jud McCranie_, Dec 23 2001

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Last modified May 30 05:35 EDT 2020. Contains 334712 sequences. (Running on oeis4.)