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A231271 Numbers n such that n and n+d are both odious (A000069) or both evil (A001969) for every divisor d of n. 3


%S 1,5,7,9,13,17,23,29,31,37,41,49,53,61,71,73,85,89,97,101,103,109,113,

%T 119,125,127,129,133,137,149,151,157,167,173,181,193,197,199,217,223,

%U 229,233,241,249,257,263,269,277,281,293,311,313,317,321,325,337,341

%N Numbers n such that n and n+d are both odious (A000069) or both evil (A001969) for every divisor d of n.

%C A prime p is a term iff its binary expansion ends in odd number of 1's (A095283). All terms are in A079523.

%H Peter J. C. Moses, <a href="/A231271/b231271.txt">Table of n, a(n) for n = 1..10000</a>

%e Odious number n=341 has divisors {1,11,31,341}. Since numbers 341+1=342, 341+11=352, 341+31=372, 341+341=682 all are odious, then 341 is in the sequence.

%t odiousQ[n_] := OddQ[DigitCount[n, 2][[1]]];selQ[n_] := Length[Union[Map[odiousQ, Flatten[{n, Map[n+#&, Divisors[n]]}]]]] == 1; Select[Range[200], selQ] (* _Peter J. C. Moses_, Nov 08 2013 *)

%Y Cf. A000069, A001969, A079523, A095283.

%K nonn,base

%O 1,2

%A _Vladimir Shevelev_, Nov 06 2013

%E More terms from _Peter J. C. Moses_, Nov 08 2013

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Last modified December 16 04:05 EST 2019. Contains 330013 sequences. (Running on oeis4.)