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A066388 Numbers n such that n and 2n are both between a pair of twin primes. 9
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 (list; graph; refs; listen; history; text; internal format)
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 2a(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.

Sequence in context: A256545 A075591 A130075 * A222718 A200894 A202861

Adjacent sequences:  A066385 A066386 A066387 * A066389 A066390 A066391

KEYWORD

nonn

AUTHOR

Jud McCranie, Dec 23 2001

STATUS

approved

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Last modified November 16 12:40 EST 2018. Contains 317272 sequences. (Running on oeis4.)