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

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

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.

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 a term because 26_10 = 222_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: A330431 A349751 A349752 * A326380 A257521 A053696

Adjacent sequences: A167779 A167780 A167781 * A167783 A167784 A167785

Keyword

nonn,base

Author

Andrew Weimholt, Nov 12 2009

Status

approved