cp's OEIS Frontend

A285575 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^2 for at least two distinct primes p.

%I A285575 #11 Apr 24 2017 00:26:03
%S A285575 1,36,2,18,4,9,8,25,12,3,24,6,30,10,20,5,40,15,45,16,27,28,7,56,14,42,
%T A285575 21,48,33,44,11,72,13,52,26,50,22,54,32,49,60,35,63,64,75,39,78,66,84,
%U A285575 51,68,17,100,19,76,38,90,34,98,46,92,23,108,29,116,58
%N A285575 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^2 for at least two distinct primes p.
%C A285575 The sequence can always be extended with a multiple of 36; after a multiple of 36, we can extend the sequence with the least unused number; as there are infinitely many multiples of 36, this sequence is a permutation of the natural numbers (with inverse A285576).
%C A285575 For any k>=0, let c_k be the lexicographically earliest sequence of distinct terms such that the product of two consecutive terms is divisible by p^2 for at least k distinct primes p; in particular we have:
%C A285575 - c_0 = A000027 (the natural numbers),
%C A285575 - c_1 = A285296,
%C A285575 - c_2 = a (this sequence).
%C A285575 For any k>=0, c_k is a permutation of the natural numbers.
%H A285575 Rémy Sigrist, <a href="/A285575/b285575.txt">Table of n, a(n) for n = 1..10000</a>
%H A285575 Rémy Sigrist, <a href="/A285575/a285575.gp.txt">PARI program for A285575</a>
%H A285575 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A285575 The first terms, alongside the primes p such that p^2 divides a(n)*a(n+1), are:
%e A285575 n       a(n)    p
%e A285575 --      ----    ----
%e A285575 1       1       2, 3
%e A285575 2       36      2, 3
%e A285575 3       2       2, 3
%e A285575 4       18      2, 3
%e A285575 5       4       2, 3
%e A285575 6       9       2, 3
%e A285575 7       8       2,    5
%e A285575 8       25      2,    5
%e A285575 9       12      2, 3
%e A285575 10      3       2, 3
%e A285575 11      24      2, 3
%e A285575 12      6       2, 3
%e A285575 13      30      2,    5
%e A285575 14      10      2,    5
%e A285575 15      20      2,    5
%e A285575 16      5       2,    5
%e A285575 17      40      2,    5
%e A285575 18      15         3, 5
%e A285575 19      45      2, 3
%e A285575 20      16      2, 3
%e A285575 ...
%e A285575 115     160     2,    5
%e A285575 116     115     2, 3, 5
%e A285575 117     180     2, 3
%e A285575 ...
%Y A285575 Cf. A285296, A285576 (inverse).
%K A285575 nonn,look
%O A285575 1,2
%A A285575 _Rémy Sigrist_, Apr 22 2017