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
a(n+1) is also the number of the circles added at the n-th iteration of the pattern generated by the construction rules: (i) At n = 0, there are six circles of radius s with centers at the vertices of a regular hexagon of side length s. (ii) At n > 0, draw a circle with center at each boundary intersection point of the figure of the previous iteration. The pattern seems to be the flower of life except at the central area. See illustration. - Kival Ngaokrajang, Oct 23 2015
LINKS
Kival Ngaokrajang, Illustration of initial terms
Sacred Geometry, Flower of life
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
a(n) = 6*A008620(n-1). - Kival Ngaokrajang, Oct 23 2015
EXAMPLE
MATHEMATICA
Table[2 n + 4 - 2 Mod[n + 2, 3], {n, 66}] (* Michael De Vlieger, Oct 23 2015 *)
PROG
(PARI) vector(200, n, n--; 6*(n\3+1)) \\ Altug Alkan, Oct 23 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, Mar 13 2000
STATUS
approved