A259675 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.

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

Offset

1,1

Links

Table of n, a(n) for n=1..35.

Example

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.

Maple

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);

Crossrefs

Cf. A003415, A244079, A258813, A258843, A259831, A259832.

Sequence in context: A237506 A264385 A167437 * A205820 A202430 A268907

Adjacent sequences: A259672 A259673 A259674 * A259676 A259677 A259678

Keyword

nonn,base

Author

Paolo P. Lava, Jul 07 2015

Status

approved