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A259675
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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.
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0
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1344, 1456, 2352, 5120, 5376, 6000, 9680, 25600, 36672, 38220, 73536, 76752, 77824, 86592, 96250, 110160, 114688, 122360, 141056, 161544, 249600, 314352, 382976, 471040, 486400, 553056, 822224, 1411536, 1525056, 1570800, 1612288, 1720320, 1886720, 2143220, 2359296
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..35.
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EXAMPLE
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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.
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.
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MAPLE
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with(numtheory): P:=proc(q) local a, b, c, k, n, p;
for n from 1 to q do c:=convert(n, binary, decimal);
for k from 1 to ilog10(c) do
a:=convert(trunc(c/10^k), decimal, binary);
b:=convert((c mod 10^k), decimal, binary);
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]);
if a*b>0 then if a*b=n then print(n);
break; fi; fi; od; od; end: P(10^9);
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CROSSREFS
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Cf. A003415, A244079, A258813, A258843, A259831, A259832.
Sequence in context: A237506 A264385 A167437 * A205820 A202430 A268907
Adjacent sequences: A259672 A259673 A259674 * A259676 A259677 A259678
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KEYWORD
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nonn,base
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AUTHOR
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Paolo P. Lava, Jul 07 2015
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STATUS
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approved
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