

A273993


Numbers whose derivative is equal to the arithmetic derivative.


2



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
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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^(i1); 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: A302566 A333702 A119153 * A225290 A065450 A090288
Adjacent sequences: A273990 A273991 A273992 * A273994 A273995 A273996


KEYWORD

nonn,easy


AUTHOR

Paolo P. Lava, Jun 08 2016


STATUS

approved



