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A274063 Numbers whose periodic derivative is equal to the arithmetic derivative. 0
0, 1, 25, 26, 51, 119, 218, 771, 1754, 1799, 1921, 7967, 16147, 32639, 128129, 196611, 458759, 1044143, 2031647, 7190234, 8323199, 33464867, 536581571, 536813567, 1073691551, 2145328183, 7202169026, 8746826298, 17179612627, 68719005499, 797299610790 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Solution of the equation A003415(n) = A038556(n).

LINKS

Table of n, a(n) for n=1..31.

EXAMPLE

25 in base 2 is 11001 and its periodic derivative is (1+1)(1+0)(0+0)(0+1)(1+1) -> 01010 that is 10 in base 10 and 10 is also the arithmetic derivative of 25.

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); b:=[1, op(b)];

for i 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);

MATHEMATICA

Select[Range[0, 10^6], Function[n, If[Abs@ n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[Abs@ n]]] == FromDigits[Thread[BitXor[#, RotateLeft@ #]], 2] &@ IntegerDigits[n, 2]]] (* Michael De Vlieger, Jun 10 2016 after Michael Somos at A003415 and Jean-Fran├žois Alcover at A038556 *)

CROSSREFS

Cf. A003415, A038556, A273993.

Sequence in context: A042260 A042262 A042264 * A042256 A042258 A042254

Adjacent sequences:  A274060 A274061 A274062 * A274064 A274065 A274066

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Jun 09 2016

EXTENSIONS

a(23)-a(31) from Giovanni Resta, Jun 19 2016

STATUS

approved

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Last modified August 6 18:25 EDT 2020. Contains 336256 sequences. (Running on oeis4.)