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URL: https://oeis.org/A066388

⇱ A066388 - OEIS

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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, 161460, 168450, 183510
OFFSET
1,1
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
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.
FORMULA
A117499(a(n)) = 4. - Reinhard Zumkeller, Mar 23 2006
{k in A014574: 2*k in A014574}. - R. J. Mathar, Jan 20 2025
EXAMPLE
j = 30 is a term since 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
Subsequence of A014574.
Subsequences: A118859, A118860, A349321.
Sequence in context: A349981 A075591 A130075 * A222718 A200894 A202861
KEYWORD
nonn
AUTHOR
Jud McCranie, Dec 23 2001
STATUS
approved