cp's OEIS Frontend

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

%I A066388 #42 Mar 13 2025 08:55:52
%S A066388 6,30,660,810,2130,2550,3330,3390,5850,6270,10530,33180,41610,44130,
%T A066388 53550,55440,57330,63840,65100,70380,70980,72270,74100,74760,78780,
%U A066388 80670,81930,87540,93240,102300,115470,124770,133980,136950,156420
%N A066388 Numbers j such that j and 2j are both between a pair of twin primes.
%C A066388 Also terms of A014574 such that twice the term is also in A014574. Related to a problem of anti-divisors.
%C A066388 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 2*a(n)+-1 divisible by 5, so only k=5m is possible. - _M. F. Hasler_, Nov 27 2010
%H A066388 Amiram Eldar, <a href="/A066388/b066388.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harry J. Smith)
%H A066388 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BitwinChain.html">Bitwin Chain</a>.
%F A066388 A117499(a(n)) = 4. - _Reinhard Zumkeller_, Mar 23 2006
%F A066388 {k in A014574: 2*k in A014574}. - _R. J. Mathar_, Jan 20 2025
%e A066388 j = 30 is a term since 29 and 31 are prime, as are 59 and 61.
%t A066388 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 A066388 (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 A066388 Subsequence of A014574.
%Y A066388 Subsequences: A118859, A118860, A349321.
%Y A066388 Cf. A001359, A006512, A117499.
%Y A066388 Cf. A118859, A118860, A349321, A348348.
%K A066388 nonn
%O A066388 1,1
%A A066388 _Jud McCranie_, Dec 23 2001