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