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A066388
Numbers j such that j and 2j are both between a pair of twin primes.
13
6, 30, 660, 810, 2130, 2550, 3330, 3390, 5850, 6270, 10530, 33180, 41610, 44130, 53550, 55440, 57330, 63840, 65100, 70380, 70980, 72270, 74100, 74760, 78780, 80670, 81930, 87540, 93240, 102300, 115470, 124770, 133980, 136950, 156420
OFFSET
1,1
COMMENTS
Also terms of A014574 such that twice the term is also in A014574. Related to a problem of anti-divisors.
A117499(a(n)) = 4. - Reinhard Zumkeller, Mar 23 2006
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
LINKS
Eric Weisstein's World of Mathematics, Bitwin Chain
EXAMPLE
For n=30, 29 and 31 are prime, as are 59 and 61.
MATHEMATICA
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 *)
PROG
(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
KEYWORD
nonn
AUTHOR
Jud McCranie, Dec 23 2001
STATUS
approved