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Owner confidence rating: High Entry average rating: Very low
Keith number (Definition)

Given a base $ b$ integer

$\displaystyle n = \sum_{i = 1}^k d_ib^{i - 1}$
where $ d_1$ is the least significant digit and $ d_k$ is the most significant, construct the sequence $ a_1 = d_k, \ldots a_k = d_1$, and for $ m > k$,
$\displaystyle a_m = \sum_{i = 1}^k a_{m - i}.$
If there is an $ x$ such that $ a_x = n$, then $ n$ is a Keith number or repfigit number.

Bibliography

1
M. Keith, ``Repfigit Numbers" J. Rec. Math. 19 (1987), 41 - 42.



"Keith number" is owned by CompositeFan. [ owner history (1) ]
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Other names:  repfigit number

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examples of Keith numbers (Example) by PrimeFan
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Cross-references: sequence, least significant digit, integer, base
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This is version 1 of Keith number, born on 2006-06-14.
Object id is 8035, canonical name is KeithNumber.
Accessed 1087 times total.

Classification:
AMS MSC: 11A63 (Number theory :: Elementary number theory :: Radix representation; digital problems)
Pending Errata and Addenda
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Discussion
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Repsylvits by Lando47 on 2006-11-01 18:05:14
Just wondring if anyone here has studied repsylvits (kind of like repfigits, but using the Silvester sequence).

In base 10 their might only be three: 13 91 adn 2551.

1, 3, 4, 13

9, 1, 10, 91

2, 5, 5, 1, 51, 2551

Ive looked upto 10^5.
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