A292833 - OEIS

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

(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