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%I #12 Mar 31 2018 16:59:06
%S 1,693,5,689,9,685,13,681,17,677,21,673,25,669,29,665,33,661,37,657,
%T 41,653,45,649,49,645,53,641,57,637,61,633,65,629,69,625,73,621,77,
%U 617,81,613,85,609,89,605,93,601,97,597,101,593,105,589,109,585,113,581
%N Lexicographically earliest sequence of distinct positive numbers such that the sum of any two consecutive terms is a pandigital number in base 5.
%C Similarly to A171102, we say that a number is pandigital in base 5 iff all digits in the set {0, 1, 2, 3, 4} appear at least once in the base 5 representation of n (leading zeros being ignored); hence we have infinitely many pandigital numbers in base 5, and this sequence is infinite.
%C The choice of base 5 is motivated by the fact that it allows the apprehension of the graphical features of the variants of this sequence in other bases, using only a few thousand terms (see also scatterplots in Links section).
%C This sequence is likely a permutation of the positive numbers.
%H Rémy Sigrist, <a href="/A292833/b292833.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A292833/a292833.png">Scatterplot of the first 1000 terms of the base 4 variant of this sequence</a>
%H Rémy Sigrist, <a href="/A292833/a292833_1.png">Scatterplot of the first 50000 terms of the base 6 variant of this sequence</a>
%H Rémy Sigrist, <a href="/A292833/a292833_2.png">Scatterplot of the first 1000000 terms of the base 7 variant of this sequence</a>
%H Rémy Sigrist, <a href="/A292833/a292833.gp.txt">PARI program for A292833</a>
%e The first terms of the sequence, alongside the sum of consecutive terms in base 5, are:
%e n a(n) a(n) + a(n+1) in base 5
%e -- ---- -----------------------
%e 1 1 10234
%e 2 693 10243
%e 3 5 10234
%e 4 689 10243
%e 5 9 10234
%e 6 685 10243
%e 7 13 10234
%e 8 681 10243
%e 9 17 10234
%e 10 677 10243
%e 11 21 10234
%e 12 673 10243
%o (PARI) See Links section.
%Y Cf. A171102.
%K nonn,base,look
%O 1,2
%A _Rémy Sigrist_, Sep 24 2017
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