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A306864 Lexicographically earliest sequence of distinct positive terms such that among the prime divisors of the product of two consecutive terms there are at least 4 runs of consecutive prime numbers.

%I A306864 #14 Mar 17 2019 21:09:37
%S A306864 1,1870,2,935,4,1045,8,1235,10,187,20,209,40,247,14,299,21,377,28,391,
%T A306864 22,85,44,95,26,115,34,55,38,65,46,91,57,182,19,110,17,220,23,130,29,
%U A306864 170,11,190,13,230,31,238,37,260,41,266,39,133,52,145,68,155,76
%N A306864 Lexicographically earliest sequence of distinct positive terms such that among the prime divisors of the product of two consecutive terms there are at least 4 runs of consecutive prime numbers.
%C A306864 This sequence is a variant of A285487.
%C A306864 This sequence is likely a permutation of the natural numbers.
%H A306864 Rémy Sigrist, <a href="/A306864/b306864.txt">Table of n, a(n) for n = 1..25000</a>
%H A306864 Rémy Sigrist, <a href="/A306864/a306864.png">Scatterplot of the first 25000 terms</a>
%H A306864 Rémy Sigrist, <a href="/A306864/a306864_1.gp.txt">PARI program for A306864</a>
%F A306864 A287170(a(n) * a(n+1)) >= 4.
%e A306864 The first terms, alongside the corresponding runs, are:
%e A306864    n   a(n)  runs in a(n)*a(n+1)
%e A306864   ---  ----  -------------------
%e A306864     1     1  2, 5, 11, 17
%e A306864     2  1870  2, 5, 11, 17
%e A306864     3     2  2, 5, 11, 17
%e A306864     4   935  2, 5, 11, 17
%e A306864     5     4  2, 5, 11, 19
%e A306864     6  1045  2, 5, 11, 19
%e A306864     7     8  2, 5, 13, 19
%e A306864     8  1235  2, 5, 13, 19
%e A306864     9    10  2, 5, 11, 17
%e A306864    10   187  2, 5, 11, 17
%e A306864    11    20  2, 5, 11, 19
%e A306864    12   209  2, 5, 11, 19
%e A306864   ...
%e A306864    32    91  3, 7, 13, 19
%e A306864    33    57  2-3, 7, 13, 19
%e A306864    34   182  2, 7, 13, 19
%e A306864   ...
%e A306864   662  1222  2, 7, 13, 47
%e A306864   663   448  2, 7, 17, 73
%e A306864   664  1241  2-3, 7-11, 17, 73
%e A306864   665   462  2-3, 7-11, 29, 43
%e A306864   666  1247  3, 17, 29, 43
%e A306864   ...
%o A306864 (PARI) See Links section.
%Y A306864 Cf. A287170, A285487.
%K A306864 nonn,look
%O A306864 1,2
%A A306864 _Rémy Sigrist_, Mar 14 2019