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A052380 a(n)=D is the smallest distance (D) between 2 non-overlapping prime-twins 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 (list; graph; refs; listen; history; text; internal format)
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 d-pattern of [d,D-d,d], where D-d=a(n)-2n is 4,2 or 0; these d-patterns 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 10-twins 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, A031924-A031938, A053319-A053331, A052350-A052358.

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

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Last modified December 22 22:37 EST 2014. Contains 252372 sequences.