

A052380


a(n)=D is the smallest distance (D) between 2 nonoverlapping primetwins differing by d=2n; these twins are [p,p+d] or [p+D,p+D+d] and p>3.


14



6, 6, 6, 12, 12, 12, 18, 18, 18, 24, 24, 24, 30, 30, 30, 36, 36, 36, 42, 42, 42, 48, 48, 48, 54, 54, 54, 60, 60, 60, 66, 66, 66, 72, 72, 72, 78, 78, 78, 84, 84, 84, 90, 90, 90, 96, 96, 96, 102, 102, 102, 108, 108, 108, 114, 114, 114, 120, 120, 120, 126, 126, 126, 132
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OFFSET

1,1


COMMENTS

For d=D the quadruple of primes becomes a triple: [p,p+d],[p+d,p+2d].
Without the p>3 condition, a(1)=2.
The starter prime p, is followed by a prime dpattern of [d,Dd,d], where Dd=a(n)2n is 4,2 or 0; these dpatterns are as follows: [2,4,2], [4,2,4], [6,6], [8,4,8], [10,2,10], [12,12], etc.
All terms of this sequence have digital root 3, 6 or 9.  J. W. Helkenberg, Jul 24 2013


LINKS

Table of n, a(n) for n=1..64.


FORMULA

a(n) = 6*Ceiling[n/3]=6*Ceiling[d/6]=D=D(n).
a(n) = 2n + 4  2((n+2) mod 3). [Wesley Ivan Hurt, Jun 30 2013]


EXAMPLE

n=5, d=2n=10, the minimal distance for 10twins is 12 (see A031928, d=10) the smallest term in A053323. It occurs first between twins of [409,419] and [421,431]; see 409 = A052354(1) = A052376(1) = A052381(5).


CROSSREFS

See also A001223, A031924A031938, A053319A053331, A052350A052358.
Sequence in context: A035019 A216057 A212096 * A180604 A109047 A153171
Adjacent sequences: A052377 A052378 A052379 * A052381 A052382 A052383


KEYWORD

nonn


AUTHOR

Labos Elemer, Mar 13 2000


STATUS

approved



