|
|
|
|
| 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.
(history;
published version)
|
|
|
|
|
#39 by Alois P. Heinz at Wed Apr 25 03:19:12 EDT 2018
|
|
|
|
|
|
|
|
#38 by Altug Alkan at Wed Apr 25 01:45:59 EDT 2018
|
|
|
|
|
|
Discussion
|
| Wed Apr 25
| 03:19
| Alois P. Heinz: yes!
|
|
|
|
|
|
|
#37 by Altug Alkan at Wed Apr 25 01:45:55 EDT 2018
|
|
| KEYWORD
|
nonn,easy,changed
|
|
| STATUS
|
proposed
editing
|
|
|
|
|
|
|
#36 by Jon E. Schoenfield at Wed Apr 25 01:22:55 EDT 2018
|
|
|
|
|
|
|
|
#35 by Jon E. Schoenfield at Wed Apr 25 01:22:52 EDT 2018
|
|
| NAME
|
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.
|
|
| COMMENTS
|
Without the p> > 3 condition, a(1)=2.
a(n+1) is also the number of the circles added at the n-th interationiteration 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
|
|
| STATUS
|
approved
editing
|
|
|
|
|
|
|
#34 by Wolfdieter Lang at Tue Oct 27 18:32:34 EDT 2015
|
|
|
|
|
|
|
|
#33 by Wolfdieter Lang at Tue Oct 27 18:32:21 EDT 2015
|
|
| COMMENTS
|
a(n+1) is also the number of the circles added at the n-th interation 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
|
|
| STATUS
|
approved
editing
|
|
|
|
|
|
|
#32 by Wolfdieter Lang at Tue Oct 27 18:29:01 EDT 2015
|
|
|
|
|
|
|
|
#31 by Jon E. Schoenfield at Sat Oct 24 06:26:41 EDT 2015
|
|
|
|
|
|
Discussion
|
| Sat Oct 24
| 09:03
| Kival Ngaokrajang: Thank you for offset editing.
|
|
|
|
|
|
|
#30 by Jon E. Schoenfield at Sat Oct 24 06:26:39 EDT 2015
|
|
| FORMULA
|
a(n) = 6*Ceiling[ceiling(n/3] = ) = 6*Ceiling[ceiling(d/6]=) = D= = D(n).
a(n) = 2n + 4 - 2((n+2) mod 3). [_). - _Wesley Ivan Hurt_, Jun 30 2013]
|
|
| STATUS
|
proposed
editing
|
|
|
|
|
|
