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%I #29 Aug 27 2024 18:17:44
%S 1,3,2,8,5,9,4,6,7,12,10,13,33,34,43,24,22,45,23,44,38,29,17,50,18,28,
%T 39,46,21,25,42,26,20,47,30,16,51,31,15,52,49,19,27,40,37,48,53,14,32,
%U 35,11,56,54,55,60,41,36,65,173,182,174,64,291,170,68,287
%N Lexicographically earliest sequence of distinct positive terms such that the sum of two consecutive terms has distinct digits in factorial base.
%C In other words, for any n > 0, a(n) + a(n+1) belongs to A321682.
%C Apparently, all the positive integers appear in the sequence.
%C This sequence has interesting graphical features (see scatterplots in Links section).
%C This sequence is to A321682 what A228730 is to A002113.
%H Rémy Sigrist, <a href="/A322845/b322845.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A322845/a322845.png">Scatterplot of the first 181425 terms</a>
%H Rémy Sigrist, <a href="/A322845/a322845_1.png">Scatterplot of the first 19958408 terms</a>
%H Rémy Sigrist, <a href="/A322845/a322845.txt">C program for A322845</a>
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%e The first terms, alongside the factorial representation of a(n)+a(n+1), are:
%e n a(n) fact(a(n)+a(n+1))
%e -- ---- -----------------
%e 1 1 (2,0)
%e 2 3 (2,1)
%e 3 2 (1,2,0)
%e 4 8 (2,0,1)
%e 5 5 (2,1,0)
%e 6 9 (2,0,1)
%e 7 4 (1,2,0)
%e 8 6 (2,0,1)
%e 9 7 (3,0,1)
%e 10 12 (3,2,0)
%e 11 10 (3,2,1)
%e 12 13 (1,3,2,0)
%o (C) // See Links section.
%Y Cf. A002113, A228730, A321682.
%K nonn,base,look
%O 1,2
%A _Rémy Sigrist_, Dec 29 2018