A273993 Numbers whose derivative is equal to the arithmetic derivative.

0, 1, 2, 10, 22, 34, 38, 46, 94, 134, 142, 158, 262, 382, 514, 526, 542, 766, 2062, 2078, 2174, 2302, 2558, 4126, 4222, 7871, 8198, 8222, 8254, 8318, 10238, 12286, 16894, 32894, 40958, 65542, 65566, 65662, 66046, 67582, 131074, 131078, 131086, 131102, 131198, 132094

Offset

1,3

Links

Paolo P. Lava, Table of n, a(n) for n = 1..78

Formula

Solution of the equation A003415(n) = A038554(n).

Example

10 in base 2 is 1010 and its derivative is (1+0)(0+1)(1+0)-> 111 that is 7 in base 10 and 7 is also the arithmetic derivative of 10.

Maple

with(numtheory): P:=proc(q) local a, b, i, n, p;
for n from 0 to q do a:=0; b:=convert(n, base, 2);
for i from 1 to nops(b)-1 do a:=a+((b[i]+b[i+1]) mod 2)*2^(i-1); od;
if a=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]) then print(n); fi;
od; end: P(10^6);

Crossrefs

Cf. A003415, A038554, A274073.

Sequence in context: A333702 A119153 A339486 * A225290 A065450 A090288

Adjacent sequences: A273990 A273991 A273992 * A273994 A273995 A273996

Keyword

nonn,easy

Author

Paolo P. Lava, Jun 08 2016

Status

approved