cp's OEIS Frontend

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.

%I A054342 #24 Apr 17 2022 03:48:25
%S A054342 5,53,211,20201,16787,69623,255803,247141,3565979,6314447,4911311,
%T A054342 12012743,23346809,43607429,34346287,36598607,51042053,460475569,
%U A054342 652576429,742585297,530324449,807620777,2988119339,12447231899,383204683,4470608101,5007182863,36589015601
%N 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.
%C A054342 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 A054342 The distances corresponding to the above terms are 2, 6, 12, 18, 24, ..., 192, 198, 204, 210, 218, 224.
%C A054342 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 A054342 Jeppe Stig Nielsen, <a href="/A054342/b054342.txt">Table of n, a(n) for n = 1..53</a> (based on A052187 b-file)
%F A054342 a(1) = A052187(1) + 2. For n>1, a(n) = A052187(n) + 6*(n-1). - _Jeppe Stig Nielsen_, Apr 16 2022
%e A054342 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 A054342 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 A054342 Here is the beginning of the table of equidistant lonely primes.
%e A054342 Equivalent to 3 consecutive primes in arithmetic progression.
%e A054342 * indicates a maximal gap. This table gives rise to A058867, A058868 and the present sequence.
%e A054342   Gap  First occurrence
%e A054342   ---  ----------------
%e A054342     2*         5
%e A054342     6*        53
%e A054342    12*       211
%e A054342    18      20201
%e A054342    24*     16787
%e A054342    30*     69623
%e A054342    36     255803
%e A054342    42*    247141
%e A054342    48*   3565979
%e A054342    54    6314447
%e A054342    60*   4911311
%e A054342    66*  12012743
%e A054342    72*  23346809
%e A054342    78   43607429
%e A054342    84*  34346287
%e A054342    90*  36598607
%e A054342    96*  51042053
%e A054342   102  460475569
%e A054342   108  652576429
%Y A054342 Cf. A006562, A052187, A058867, A058868, A103709.
%K A054342 nonn
%O A054342 1,1
%A A054342 _Harvey P. Dale_, May 06 2000
%E A054342 More terms from _Jud McCranie_, Jun 13 2000
%E A054342 Further terms from Harvey Dubner (harvey(AT)dubner.com), Sep 11 2004
%E A054342 Entry revised by _N. J. A. Sloane_, Jul 23 2006
%E A054342 4 further terms from Walter Neumann (neumann(AT)math.columbia.edu), Aug 14 2006
%E A054342 a(28) corrected, and terms after a(28) moved from Data section to b-file by _Jeppe Stig Nielsen_, Apr 16 2022