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 A288164 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, a(n)*a(n+2) has at least 5 distinct prime factors. 3
 1, 2, 2310, 1155, 3, 4, 770, 1365, 6, 8, 385, 1785, 12, 10, 455, 231, 18, 20, 595, 273, 22, 30, 105, 77, 26, 60, 165, 91, 14, 66, 195, 35, 28, 78, 255, 55, 38, 42, 210, 65, 11, 84, 390, 85, 7, 114, 330, 70, 13, 33, 420, 130, 17, 21, 462, 110, 5, 39, 546, 140 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence is a permutation of the natural numbers, with inverse A288799. Conjecturally, a(n) ~ n. For k >= 0, let f_k be the lexicographically earliest sequence of distinct positive terms such that, for any n > 0, a(n)*a(n+k) has at least 5 distinct prime factors. In particular, we have: - f_0 = the numbers with at least 5 distinct prime factors, - f_1 = A285487, - f_2 = a (this sequence), - f_3 = A288171. If k > 0, then: - f_k is a permutation of the natural numbers, - f_k(i) = i for any i <= k, - f_k(k+1) = A002110(5), - conjecturally, f_k(n) ~ n. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..25000 Rémy Sigrist, C++ program for A288164 EXAMPLE The first terms, alongside the primes p dividing a(n)*a(n+2), are: n       a(n)    p --      ----    -------------- 1       1       2, 3, 5, 7, 11 2       2       2, 3, 5, 7, 11 3       2310    2, 3, 5, 7, 11 4       1155    2, 3, 5, 7, 11 5       3       2, 3, 5, 7, 11 6       4       2, 3, 5, 7,     13 7       770     2, 3, 5, 7, 11 8       1365    2, 3, 5, 7,     13 9       6       2, 3, 5, 7, 11 10      8       2, 3, 5, 7,         17 11      385     2, 3, 5, 7, 11 12      1785    2, 3, 5, 7,         17 13      12      2, 3, 5, 7,     13 14      10      2, 3, 5, 7, 11 15      455     2, 3, 5, 7,     13 16      231     2, 3, 5, 7, 11 17      18      2, 3, 5, 7,         17 18      20      2, 3, 5, 7,     13 19      595     2,    5, 7, 11,     17 20      273     2, 3, 5, 7,     13 21      22      2, 3, 5, 7, 11 22      30      2, 3, 5, 7, 11 23      105     2, 3, 5, 7,     13 CROSSREFS Cf. A002110, A285487, A288171, A288799 (inverse). Sequence in context: A005800 A200170 A280899 * A133074 A280312 A276650 Adjacent sequences:  A288161 A288162 A288163 * A288165 A288166 A288167 KEYWORD nonn,look AUTHOR Rémy Sigrist, Jun 16 2017 STATUS approved

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Last modified October 23 17:19 EDT 2019. Contains 328373 sequences. (Running on oeis4.)