cp's OEIS Frontend

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

%I A167782 #25 Aug 20 2025 16:45:09
%S A167782 0,7,13,15,21,26,31,40,42,43,57,62,63,73,80,85,86,91,93,111,114,121,
%T A167782 124,127,129,133,146,156,157,170,171,172,182,183,211,215,219,222,228,
%U A167782 241,242,255,259,266,273,285,292,307,312,314,333,341,342,343,364,365,366
%N A167782 Numbers that are repdigits with length > 2 in some base.
%C A167782 Definition requires "length > 2" because all numbers n > 2 are trivially represented as "11" in base n-1.
%C A167782 0 included at the suggestion of _Franklin T. Adams-Watters_ (and others) as 0 = 000 in any base.
%H A167782 Vojtech Strnad, <a href="/A167782/b167782.txt">Table of n, a(n) for n = 1..10000</a>
%H A167782 Wolfram Demonstrations Project, <a href="http://demonstrations.wolfram.com/MixedRadixNumberRepresentations/">Mixed Radix Number Representations</a> [From _Daniel Forgues_, Nov 13 2009]
%e A167782 26 is a term because 26_10 = 222_3.
%o A167782 (PARI) /* In PARI versions < 2.6, define: digits(n,b) = if(n<b, [n], concat(digits(floor(n/b),b),n%b)) */
%o A167782 is_repdigit(d) = {local(a,r);r=1;a=d[1];for(i=2,matsize(d)[2],if(a!=d[i],r=0));r}
%o A167782 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_
%Y A167782 Cf. A010785 (Repdigits (base 10)).
%Y A167782 Cf. A167783 (Numbers that are repdigits with length > 2 in more than one base).
%Y A167782 Cf. A053696 (Numbers which are repunits in some base).
%Y A167782 Cf. A158235 (Numbers n whose square can be represented as a repdigit number in some base < n).
%K A167782 nonn,base
%O A167782 1,2
%A A167782 _Andrew Weimholt_, Nov 12 2009