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 A280659 #66 Apr 10 2019 07:25:50 %S A280659 1,2309,421,1889,841,1469,1261,1049,1681,629,2101,209,2521,1769,541, %T A280659 2189,121,2609,961,1349,1381,929,1801,509,2221,89,2641,1649,661,2069, %U A280659 241,2489,1081,1229,1501,809,1921,389,2341,1949,361,2369,1201,1109,1621,689,2041 %N A280659 Lexicographically earliest sequence of distinct positive terms such that the sum of two consecutive terms has at least 5 distinct prime factors. %C A280659 Conjecturally: this sequence is a permutation of the natural numbers, and a(n) ~ n. %C A280659 The first fixed points are: 1, 7379, 7730, 7765, 7846, 9535, 9903, 11604, 11631, 11741, 12674, 15549, 15824, 16670, 16745, 16800, 16806, 16841. %C A280659 This sequence has similarities with A285487: here we consider the sum of consecutive terms, there the product of consecutive terms. %C A280659 From _Rémy Sigrist_, Jul 16 2017: (Start) %C A280659 The scatterplot of the first terms presents rectangular clusters of points near the origin; these clusters seem to correspond to indexes n satisfying a(n) + a(n+1) < 2 * prime#(5) (where prime(k)# = A002110(k)). %C A280659 Near the origin, we also have ranges of more than hundred consecutive terms where the function b satisfying b(n) = lpf(a(n)) (where lpf = A020639) is constant (and equals 2, 3 or 5). %C A280659 These features are highlighted in the alternate scatterplots provided in the Links section. %C A280659 There features are also visible in the scatterplots of variants of this sequence where we increase the minimum number of distinct prime factors required for the sum of two consecutive terms. %C A280659 (End) %H A280659 Rémy Sigrist, <a href="/A280659/b280659.txt">Table of n, a(n) for n = 1..10000</a> %H A280659 Rémy Sigrist, <a href="/A280659/a280659.gp.txt">PARI program for A280659</a> %H A280659 Rémy Sigrist, <a href="/A280659/a280659.png">Scatterplot of the first 10000 terms, highlighting the rectangular clusters near the origin</a> %H A280659 Rémy Sigrist, <a href="/A280659/a280659_1.png">Scatterplot of the first 10000 terms, highlighting lpf(a(n)) = 2, 3 or 5</a> %e A280659 The first terms, alongside the primes p dividing a(n)+a(n+1), are: %e A280659 n a(n) p %e A280659 -- ---- -------------- %e A280659 1 1 2, 3, 5, 7, 11 %e A280659 2 2309 2, 3, 5, 7, 13 %e A280659 3 421 2, 3, 5, 7, 11 %e A280659 4 1889 2, 3, 5, 7, 13 %e A280659 5 841 2, 3, 5, 7, 11 %e A280659 6 1469 2, 3, 5, 7, 13 %e A280659 7 1261 2, 3, 5, 7, 11 %e A280659 8 1049 2, 3, 5, 7, 13 %e A280659 9 1681 2, 3, 5, 7, 11 %e A280659 10 629 2, 3, 5, 7, 13 %e A280659 11 2101 2, 3, 5, 7, 11 %e A280659 12 209 2, 3, 5, 7, 13 %e A280659 13 2521 2, 3, 5, 11, 13 %e A280659 14 1769 2, 3, 5, 7, 11 %e A280659 15 541 2, 3, 5, 7, 13 %e A280659 16 2189 2, 3, 5, 7, 11 %e A280659 17 121 2, 3, 5, 7, 13 %e A280659 18 2609 2, 3, 5, 7, 17 %e A280659 19 961 2, 3, 5, 7, 11 %e A280659 20 1349 2, 3, 5, 7, 13 %Y A280659 Cf. A002110, A020639, A285487. %K A280659 nonn,look %O A280659 1,2 %A A280659 _Rémy Sigrist_, Apr 25 2017