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Numbers such that the digital sums in bases 2, 3, 5 and 10 all are equal.
1

%I #8 Mar 30 2024 11:38:46

%S 1,12250,12251,23230,23231,32410,32411,45010,45011,51130,51131,52030,

%T 52031,54010,54011,100053,100090,100091,100305,102250,102251,107002,

%U 107003,110134,110170,110171,110350,110351,110460,110461,113050,113051

%N Numbers such that the digital sums in bases 2, 3, 5 and 10 all are equal.

%H G. C. Greubel, <a href="/A135128/b135128.txt">Table of n, a(n) for n = 1..700</a>

%e a(2)=12250 since ds_2(12250 )=ds_3(12250 )=ds_5(12250 )=ds_10(12250 )=10, where ds_x=digital sum base x.

%t Select[Range[32000], Total[IntegerDigits[#, 2]] == Total[IntegerDigits[#, 3]] == Total[IntegerDigits[#, 5]] == Total[IntegerDigits[#, 10]] &] (* _G. C. Greubel_, Sep 28 2016 *)

%t Select[Range[120000],Length[Union[Total/@IntegerDigits[#,{2,3,5,10}]]]==1&] (* _Harvey P. Dale_, Mar 30 2024 *)

%Y Cf. A007953, A054899, A131451, A133620, A133900, A134599, A135100, A135110, A135120, A037308.

%K nonn,base

%O 1,2

%A _Hieronymus Fischer_, Dec 31 2007