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, 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

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