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 A255734 Numbers n such that A080719(n) divides n. 0

%I #11 Apr 02 2019 03:04:56

%S 1,2,3,4,5,6,7,8,9,10,12,20,30,40,50,60,70,80,90,100,105,112,120,200,

%T 210,220,240,300,330,342,360,400,408,453,462,500,504,573,600,700,720,

%U 800,900,924,1000,1008,1010,1012,1020,1040,1050,1116,1120,1145,1200,1320,1750,1900,2000

%N Numbers n such that A080719(n) divides n.

%e Let us consider n = 342: 3 converted to base 2 is 11, 4 is 100, 2 is 10. Their concatenation is 1110010 that converted to base 10 is 114. So A080719(342) = 114. Finally 114 divides 342, so 342 is a member.

%p P:=proc(q) local a,b,k,n,x; for n from 1 to q do x:=[]; a:=n;

%p for k from 1 to length(n) do b:=convert((a mod 10), base, 2);

%p if b=[] then x:=[op(x),0]; else x:=[op(x),op(b)]; fi; a:=trunc(a/10); od; a:=0;

%p for k from 1 to nops(x) do a:=2*a+x[-k]; od; if frac(n/a)=0 then print(n);

%p fi; od; end: P(2000);

%t Select[Range[2000],Divisible[#,FromDigits[Flatten[IntegerDigits[#,2]&/@ IntegerDigits[ #]],2]]&] (* _Harvey P. Dale_, Mar 13 2019 *)

%Y Cf. A007088, A080719.

%K nonn,base

%O 1,2

%A _Paolo P. Lava_, Mar 05 2015

%E Corrected and extended by _Harvey P. Dale_, Mar 13 2019

%E Corrected Maple code by _Paolo P. Lava_, Apr 01 2019

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Last modified June 20 19:46 EDT 2024. Contains 373532 sequences. (Running on oeis4.)