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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-François 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 12 18:44 EDT 2024. Contains 375113 sequences. (Running on oeis4.)