|
Search: id:A054342
|
|
|
| A054342 |
|
First occurrence of distances of equidistant lonely primes. Each equidistant prime is at the same distance (or has the same gap) from the preceding prime and the next prime. |
|
+0
7
|
|
| 5, 53, 211, 20201, 16787, 69623, 255803, 247141, 3565979, 6314447, 4911311, 12012743, 23346809, 43607429, 34346287, 36598607, 51042053, 460475569, 652576429, 742585297, 530324449, 807620777, 2988119339, 12447231899, 383204683, 4470608101, 5007182863, 71015248091, 5558570491, 88526967847, 65997364621, 48287689717, 57484162331, 50284155289, 178796541817, 264860525507, 978720895253, 472446412421, 374787490919
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Or, least balanced primes: the smallest prime p[n] such that the distances to the next smallest and next largest primes are both equal to 6n.
The distances corresponding to the above terms are 2,6,12,18,24...192,198,204.
|
|
EXAMPLE
|
211 is an equidistant lonely prime with distance 12. This is the first occurrence of the distance 12, thus 211 is in the sequence.
20201 is a least balanced prime because it is the third term in the sequence and is separated from both the next lower and next higher primes by 3 x 6 = 18.
Here is the beginning of the table of equidistant lonely primes.
Equivalent to 3 consecutive primes in arithmetic progression.
* indicates a maximal gap. This table gives rise to A058867, A058868 and the present sequence.
Gap First occurrence
--- ----------------
2* 5
6* 53
12* 211
18 20201
24* 16787
30* 69623
36 255803
42* 247141
48* 3565979
54 6314447
60* 4911311
66* 12012743
72* 23346809
78 43607429
84* 34346287
90* 36598607
96* 51042053
102 460475569
108 652576429
|
|
CROSSREFS
|
Cf. A058867, A058868, A006562, A103709.
Adjacent sequences: A054339 A054340 A054341 this_sequence A054343 A054344 A054345
Sequence in context: A094852 A058867 A058869 this_sequence A068170 A069632 A069617
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Harvey P. Dale (hpd1(AT)is2.nyu.edu), May 06 2000
|
|
EXTENSIONS
|
More terms from Jud McCranie (j.mccranie(AT)comcast.net), Jun 13 2000
Further terms from Harvey Dubner (harvey(AT)dubner.com), Sep 11 2004
Entry revised by njas, Jul 23 2006
4 further terms from Walter Neumann (neumann(AT)math.columbia.edu), Aug 14 2006
|
|
|
Search completed in 0.002 seconds
|
