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

Author

Jud McCranie, Dec 23 2001

Keywords

• nonn

Comments

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

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

Examples

			j = 30 is a term since 29 and 31 are prime, as are 59 and 61.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)
• Eric Weisstein's World of Mathematics, Bitwin Chain.

Crossrefs

Subsequence of A014574.

Subsequences: A118859, A118860, A349321.

Cf. A001359, A006512, A117499.

Cf. A118859, A118860, A349321, A348348.

Programs

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 *)

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

Formula

A117499(a(n)) = 4. - Reinhard Zumkeller, Mar 23 2006

{k in A014574: 2*k in A014574}. - R. J. Mathar, Jan 20 2025