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%I #8 Dec 27 2019 05:21:27
%S 13,26,29,52,53,55,58,61,77,103,104,106,109,110,111,116,117,119,122,
%T 125,154,157,205,206,207,208,212,213,215,218,219,220,221,222,223,231,
%U 232,234,237,238,239,244,245,247,250,253,308,309,311,314,317,333,359,365
%N In binary expansion, number of 1's in 5n is less than in n.
%C Or, binary weight of 5n is less than binary weight of n.
%C Also called the 5-flimsy numbers; see the Stolarsky reference.
%C If m is here, 2m is too. Hence the "primitive solutions" are all odd ones:
%C 13,29,53,55,61,77,103,109,111,117,119,125,157,205,207,213,215,219,221,223,231.
%H Kenneth B. Stolarsky, <a href="https://eudml.org/doc/205727">Integers whose multiples have anomalous digital frequencies</a>, Acta Arithmetica 38 (2) (1980), 117-128.
%F A000120(n) > A000120(5n).
%t Select[Range[1000],Count[IntegerDigits[5#,2],1]<Count[IntegerDigits[ #,2],1]&]
%o (PARI) for(k=1,370, if(hammingweight(5*k) < hammingweight(k), print1(k,", "))) \\ _Hugo Pfoertner_, Dec 27 2019
%Y Cf. A000120, A005360, A180054.
%K base,nonn
%O 1,1
%A _Zak Seidov_, Aug 08 2010
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