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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 25 20:04 EST 2020. Contains 332258 sequences. (Running on oeis4.)