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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 (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.

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

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Last modified September 23 05:06 EDT 2019. Contains 327327 sequences. (Running on oeis4.)