Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three Cousins of Recaman's Sequence   Although 10^230 terms of Recaman's sequence have been computed, it remains a
mystery. Here three distant cousins of that sequence are described, one of
which is also mysterious. (i) {A(n), n >= 3} is defined as follows. Start with
n, and add n+1, n+2, n+3, ..., stopping after adding n+k if the sum n + (n+1) +
... + (n+k) is divisible by n+k+1. Then A(n)=k. We determine A(n) and show that
A(n) <= n^2 - 2n - 1. (ii) {B(n), n >= 1} is a multiplicative analog of {A(n)}.
Start with n, and successively multiply by n+1, n+2, ..., stopping after
multiplying by n+k if the product n(n+1)...(n+k) is divisible by n+k+1. Then
B(n)=k. We conjecture that log^2 B(n) = (1/2 + o(1)) log n loglog n. (iii) The
third sequence, {C(n), n >= 1}, is the most interesting, because the most
mysterious. Concatenate the decimal digits of n, n+1, n+2, ... until the
concatenation n||n+1||...||n+k is divisible by n+k+1. Then C(n)=k. If no such k
exists we set C(n)=-1. We have found k for all n <= 1000 except for two cases.
Some of the numbers involved are quite large. For example, C(92) =
218128159460, and the concatenation 92||93||...||(92+C(92)) is a number with
about 2*10^12 digits. We have only a probabilistic argument that such a k
exists for all n.

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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: math-ph