This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A285655 #15 Jun 14 2017 02:47:02 %S A285655 1,30030,2,15015,4,19635,6,5005,12,6545,18,7315,24,7735,22,1365,34, %T A285655 1155,26,1785,38,2145,14,2805,28,3135,42,715,84,935,78,385,102,455,66, %U A285655 595,114,770,39,1190,33,910,51,1330,69,1430,21,1870,57,1540,87,1610,93 %N A285655 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms has at least 6 distinct prime factors. %C A285655 This sequence can always be extended with a multiple of 30030 = 2*3*5*7*11*13; after a term that has at least 6 distinct prime factors, we can extend the sequence with the least unused number; as there are infinitely many numbers with at least 6 distinct prime factors, this sequence is a permutation of the natural numbers (with inverse A285656). %C A285655 Conjecturally, a(n) ~ n. %C A285655 The first fixed points are: 1, 39, 1344, 1350, 3556, 3560, 5738, 6974, 15668585, 15668673, 15668787. %C A285655 For any k>0, let d_k be the lexicographically earliest sequence of distinct terms such that the product of two consecutive terms has at least k distinct prime factors; in particular we have: %C A285655 - d_1 = A000027 (the natural numbers), %C A285655 - d_5 = A285487, %C A285655 - d_6 = a (this sequence). %C A285655 For any k>0: %C A285655 - d_k is a permutation of the natural numbers, %C A285655 - d_k(1) = 1 and d_k(2) = A002110(k), %C A285655 - conjecturally: d_k(n) ~ n. %H A285655 Rémy Sigrist, <a href="/A285655/b285655.txt">Table of n, a(n) for n = 1..10000</a> %H A285655 Rémy Sigrist, <a href="/A285655/a285655.png">Scatterplot of the first 20 000 000 terms</a> %H A285655 Rémy Sigrist, <a href="/A285655/a285655_1.png">Scatterplot of the first difference of the first 20 000 000 terms</a> %H A285655 Rémy Sigrist, <a href="/A285655/a285655.txt">C++ program for A285655</a> %H A285655 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a> %e A285655 The first terms, alongside the primes p dividing a(n)*a(n+1), are: %e A285655 n a(n) p %e A285655 -- ---- ------------------ %e A285655 1 1 2, 3, 5, 7, 11, 13 %e A285655 2 30030 2, 3, 5, 7, 11, 13 %e A285655 3 2 2, 3, 5, 7, 11, 13 %e A285655 4 15015 2, 3, 5, 7, 11, 13 %e A285655 5 4 2, 3, 5, 7, 11, 17 %e A285655 6 19635 2, 3, 5, 7, 11, 17 %e A285655 7 6 2, 3, 5, 7, 11, 13 %e A285655 8 5005 2, 3, 5, 7, 11, 13 %e A285655 9 12 2, 3, 5, 7, 11, 17 %e A285655 10 6545 2, 3, 5, 7, 11, 17 %e A285655 11 18 2, 3, 5, 7, 11, 19 %e A285655 12 7315 2, 3, 5, 7, 11, 19 %e A285655 13 24 2, 3, 5, 7, 13, 17 %e A285655 14 7735 2, 5, 7, 11, 13, 17 %e A285655 15 22 2, 3, 5, 7, 11, 13 %e A285655 16 1365 2, 3, 5, 7, 13, 17 %e A285655 17 34 2, 3, 5, 7, 11, 17 %e A285655 18 1155 2, 3, 5, 7, 11, 13 %e A285655 19 26 2, 3, 5, 7, 13, 17 %e A285655 20 1785 2, 3, 5, 7, 17, 19 %Y A285655 Cf. A000027, A002110, A285487, A285656 (inverse). %K A285655 nonn %O A285655 1,2 %A A285655 _Rémy Sigrist_, Apr 23 2017