

A292833


Lexicographically earliest sequence of distinct positive numbers such that the sum of any two consecutive terms is a pandigital number in base 5.


1



1, 693, 5, 689, 9, 685, 13, 681, 17, 677, 21, 673, 25, 669, 29, 665, 33, 661, 37, 657, 41, 653, 45, 649, 49, 645, 53, 641, 57, 637, 61, 633, 65, 629, 69, 625, 73, 621, 77, 617, 81, 613, 85, 609, 89, 605, 93, 601, 97, 597, 101, 593, 105, 589, 109, 585, 113, 581
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OFFSET

1,2


COMMENTS

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.
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).
This sequence is likely a permutation of the positive numbers.


LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Scatterplot of the first 1000 terms of the base 4 variant of this sequence
Rémy Sigrist, Scatterplot of the first 50000 terms of the base 6 variant of this sequence
Rémy Sigrist, Scatterplot of the first 1000000 terms of the base 7 variant of this sequence
Rémy Sigrist, PARI program for A292833


EXAMPLE

The first terms of the sequence, alongside the sum of consecutive terms in base 5, are:
n a(n) a(n) + a(n+1) in base 5
  
1 1 10234
2 693 10243
3 5 10234
4 689 10243
5 9 10234
6 685 10243
7 13 10234
8 681 10243
9 17 10234
10 677 10243
11 21 10234
12 673 10243


PROG

(PARI) See Links section.


CROSSREFS

Cf. A171102.
Sequence in context: A290010 A037149 A196894 * A004240 A004241 A322154
Adjacent sequences: A292830 A292831 A292832 * A292834 A292835 A292836


KEYWORD

nonn,base,look


AUTHOR

Rémy Sigrist, Sep 24 2017


STATUS

approved



