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A167782 Numbers that are repdigits with length > 2 in some base. 2
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 n-1.

0 included at the suggestion of Franklin T. Adams-Watters (and others) as 0 = 000 in any base.

Contribution 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

Table of n, a(n) for n=1..57.

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, from Michael Porter) 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++))

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

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Last modified March 30 14:19 EDT 2017. Contains 284302 sequences.