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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. 8

%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

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Last modified November 17 00:08 EST 2019. Contains 329209 sequences. (Running on oeis4.)