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

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

Harry J. Smith, Table of n, a(n) for n = 1..1000

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

Crossrefs

Cf. A001359, A006512, A012574.

Cf. A014574, A118859, A118860, A349321, A348348.

Sequence in context: A349981 A075591 A130075 * A222718 A200894 A202861

Adjacent sequences: A066385 A066386 A066387 * A066389 A066390 A066391

Keyword

nonn

Author

Jud McCranie, Dec 23 2001

Status

approved