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A292833
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Lexicographically earliest sequence of distinct positive numbers such that the sum of any two consecutive terms is a pandigital number in base 5.
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1
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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
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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