|
%I #24 Jul 17 2015 12:30:41
%S 1344,1456,2352,5120,5376,6000,9680,25600,36672,38220,73536,76752,
%T 77824,86592,96250,110160,114688,122360,141056,161544,249600,314352,
%U 382976,471040,486400,553056,822224,1411536,1525056,1570800,1612288,1720320,1886720,2143220,2359296
%N Numbers n with the property that it is possible to write the base 2 expansion of n as concat(a_2,b_2), with a_2>0 and b_2>0 such that, converting a_2 and b_2 to base 10 as a and b, we have a’ * b’ = n, where a’ and b’ are the arithmetic derivatives of a and b.
%e 1344 in base 2 is 10101000000. If we take 10101000000 = concat(1010, 1000000) then 1010 and 1000000 converted to base 10 are 10 and 64. Their arithmetic derivatives are 7 and 192. Finally 7 * 192 = 1344.
%e 1456 in base 2 is 10110110000. If we take 10110110000 = concat(10110, 110000) then 10110 and 110000 converted to base 10 are 22 and 48. Their arithmetic derivatives are 13 and 112. Finally 13 * 112 = 1456.
%p with(numtheory): P:=proc(q) local a,b,c,k,n,p;
%p for n from 1 to q do c:=convert(n,binary,decimal);
%p for k from 1 to ilog10(c) do
%p a:=convert(trunc(c/10^k),decimal,binary);
%p b:=convert((c mod 10^k),decimal,binary);
%p a:=a*add(op(2,p)/op(1,p),p=ifactors(a)[2]); b:=b*add(op(2,p)/op(1,p),p=ifactors(b)[2]);
%p if a*b>0 then if a*b=n then print(n);
%p break; fi; fi; od; od; end: P(10^9);
%Y Cf. A003415, A244079, A258813, A258843, A259831, A259832.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_, Jul 07 2015
|
