

A167782


Numbers that are repdigits with length > 2 in some base.


15



0, 7, 13, 15, 21, 26, 31, 40, 42, 43, 57, 62, 63, 73, 80, 85, 86, 91, 93, 111, 114, 121, 124, 127, 129, 133, 146, 156, 157, 170, 171, 172, 182, 183, 211, 215, 219, 222, 228, 241, 242, 255, 259, 266, 273, 285, 292, 307, 312, 314, 333, 341, 342, 343, 364, 365, 366
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OFFSET

1,2


COMMENTS

Definition requires "length > 2" because all numbers n > 2 are trivially represented as "11" in base n1.
0 included at the suggestion of Franklin T. AdamsWatters (and others) as 0 = 000 in any base.
From Daniel Forgues, Nov 13 2009: (Start)
0 = 00 = 000 = 0000 = 00000 = 000000 = 0000000 = 00000000 = ... in any positional number representation (includes fixed base radix b > 1, mixed base radix with each b_i > 1, i >= 0, such as factorial and primorial based radix...)
The sequence definition should be read as:
Nonnegative integers that are repdigits with length > 2 in at least one fixed base radix b > 1.
Considering all fixed and mixed base radix would include many more nonnegative integers (but not the integers 1 to 6) which are repdigits with length > 2. (End)


LINKS

Vojtech Strnad, Table of n, a(n) for n = 1..10000
Wolfram Demonstrations Project, Mixed Radix Number Representations [From Daniel Forgues, Nov 13 2009]


EXAMPLE

26 is in the list because 26 (base 10) = 222 (base 3)


PROG

(PARI) digits(n, b) = if(n<b, [n], concat(digits(floor(n/b), b), n%b))
is_repdigit(d) = {local(a, r); r=1; a=d[1]; for(i=2, matsize(d)[2], if(a!=d[i], r=0)); r}
for(n=1, 1200, b=2; while(n>=b^2+b+1, d=digits(n, b); if(is_repdigit(d), print(n, " = ", d, " base ", b)); b++)) \\ Michael B. Porter


CROSSREFS

Cf. A010785  Repdigits (base 10)
Cf. A167783  Numbers that are repdigits with length > 2 in more than one base.
Cf. A053696  Numbers which are repunits in some base
Cf. A158235  Numbers n whose square can be represented as a repdigit number in some base < n
Sequence in context: A076701 A224773 A076196 * A326380 A257521 A053696
Adjacent sequences: A167779 A167780 A167781 * A167783 A167784 A167785


KEYWORD

nonn,base


AUTHOR

Andrew Weimholt, Nov 12 2009


STATUS

approved



