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A138299 For number bases b (2 <= b <= 10) consider numbers that can be written as repdigits with at least two digits: the sequence gives products of such numbers also having this property (the number bases are not necessarily distinct).

%I A138299 #8 Feb 16 2025 08:33:07
%S A138299 9,12,15,16,18,20,21,24,27,28,30,32,33,35,36,40,42,44,45,48,50,54,55,
%T A138299 60,63,66,70,77,80,88,91,93,99,121,124,129,156,171,172,182,215,219,
%U A138299 228,242,255,273,285,292,312,333,341,342,364,365,400,438,444,455,468,511,546
%N A138299 For number bases b (2 <= b <= 10) consider numbers that can be written as repdigits with at least two digits: the sequence gives products of such numbers also having this property (the number bases are not necessarily distinct).
%H A138299 R. Zumkeller, <a href="/A138299/b138299.txt">Table of n, a(n) for n = 1..250</a>
%H A138299 R. Zumkeller, <a href="/A138299/a138299.txt">RepDigit Products</a>
%H A138299 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RepeatingDecimal.html">Repeating Decimal</a>
%H A138299 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Base.html">Base</a>
%e A138299 a(20) = 48 = 3*16:     66_7  =  11_2 *  22_7;
%e A138299 a(21) = 50 = 5*10:     55_9  =  11_4 *  22_4;
%e A138299 a(22) = 54 = 3*18:     66_8  =  11_2 *  33_5;
%e A138299 a(23) = 55 = 5*11:     55_10 =  11_4 *  11_10;
%e A138299 a(24) = 60 = 3*20:     66_9  =  11_2 *  22_9;
%e A138299 a(25) = 63 = 3*21: 111111_2  =  11_2 * 111_4;
%e A138299 a(26) = 66 = 3*22:     66_10 =  11_2 *  22_10;
%e A138299 a(27) = 70 = 5*14:     77_9  =  11_4 *  22_6;
%e A138299 a(28) = 77 = 7*11:     77_10 = 111_2 *  11_10;
%e A138299 a(29) = 80 = 4*20:   2222_3  =  11_3 *  22_9.
%K A138299 nonn,base
%O A138299 1,1
%A A138299 _Reinhard Zumkeller_, Mar 14 2008