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%I #24 Apr 17 2022 03:48:25
%S 5,53,211,20201,16787,69623,255803,247141,3565979,6314447,4911311,
%T 12012743,23346809,43607429,34346287,36598607,51042053,460475569,
%U 652576429,742585297,530324449,807620777,2988119339,12447231899,383204683,4470608101,5007182863,36589015601
%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.
%C 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
%H Jeppe Stig Nielsen, <a href="/A054342/b054342.txt">Table of n, a(n) for n = 1..53</a> (based on A052187 b-file)
%F a(1) = A052187(1) + 2. For n>1, a(n) = A052187(n) + 6*(n-1). - _Jeppe Stig Nielsen_, Apr 16 2022
%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 * 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. A006562, A052187, A058867, A058868, 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
%E a(28) corrected, and terms after a(28) moved from Data section to b-file by _Jeppe Stig Nielsen_, Apr 16 2022
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