%I
%S 5,53,211,20201,16787,69623,255803,247141,3565979,6314447,4911311,
%T 12012743,23346809,43607429,34346287,36598607,51042053,460475569,
%U 652576429,742585297,530324449,807620777,2988119339,12447231899,383204683,4470608101,5007182863,71015248091,5558570491,88526967847,65997364621,48287689717,57484162331,50284155289,178796541817,264860525507,978720895253,472446412421,374787490919
%N 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.
%C 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.
%C The distances corresponding to the above terms are 2,6,12,18,24...192,198,204,210,218,224.
%e 211 is an equidistant lonely prime with distance 12. This is the first occurrence of the distance 12, thus 211 is in the sequence.
%e 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.
%e Here is the beginning of the table of equidistant lonely primes.
%e Equivalent to 3 consecutive primes in arithmetic progression.
%e * indicates a maximal gap. This table gives rise to A058867, A058868 and the present sequence.
%e Gap First occurrence
%e  
%e 2* 5
%e 6* 53
%e 12* 211
%e 18 20201
%e 24* 16787
%e 30* 69623
%e 36 255803
%e 42* 247141
%e 48* 3565979
%e 54 6314447
%e 60* 4911311
%e 66* 12012743
%e 72* 23346809
%e 78 43607429
%e 84* 34346287
%e 90* 36598607
%e 96* 51042053
%e 102 460475569
%e 108 652576429
%Y Cf. A058867, A058868, A006562, A103709.
%K nonn
%O 1,1
%A _Harvey P. Dale_, May 06 2000
%E More terms from _Jud McCranie_, Jun 13 2000
%E Further terms from Harvey Dubner (harvey(AT)dubner.com), Sep 11 2004
%E Entry revised by _N. J. A. Sloane_, Jul 23 2006
%E 4 further terms from Walter Neumann (neumann(AT)math.columbia.edu), Aug 14 2006
