

A167782


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


4



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 * A257521 A053696 A090503
Adjacent sequences: A167779 A167780 A167781 * A167783 A167784 A167785


KEYWORD

nonn,base


AUTHOR

Andrew Weimholt, Nov 12 2009


STATUS

approved



