OFFSET
1,1
COMMENTS
Or, least balanced primes: starting with 2nd term, 53, the smallest prime 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, 210, 218, 224.
a(1) is the smallest prime p such that {p-2, p, p+2} are three consecutive primes. For n>1, a(n) is the smallest prime p such that {p-6*(n-1), p, p+6*(n-1)} are three consecutive primes. - Jeppe Stig Nielsen, Apr 16 2022
LINKS
Jeppe Stig Nielsen, Table of n, a(n) for n = 1..53 (based on A052187 b-file)
FORMULA
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 * 6 = 18.
Here is the beginning of the table of equidistant lonely primes.
Equivalent to 3 consecutive primes in arithmetic progression.
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
KEYWORD
nonn
AUTHOR
Harvey P. Dale, May 06 2000
EXTENSIONS
More terms from Jud McCranie, Jun 13 2000
Further terms from Harvey Dubner (harvey(AT)dubner.com), Sep 11 2004
Entry revised by N. J. A. Sloane, Jul 23 2006
4 further terms from Walter Neumann (neumann(AT)math.columbia.edu), Aug 14 2006
a(28) corrected, and terms after a(28) moved from Data section to b-file by Jeppe Stig Nielsen, Apr 16 2022
STATUS
approved