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A322845 Lexicographically earliest sequence of distinct positive terms such that the sum of two consecutive terms has distinct digits in factorial base.

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