A322845 - OEIS

%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