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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 (list; graph; refs; listen; history; text; internal format)
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: 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

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Last modified September 30 22:26 EDT 2020. Contains 337440 sequences. (Running on oeis4.)