%I #9 Nov 19 2013 13:34:57

%S 59,103,193,229,251,313,431,761,929,1019,1087,1279,1367,1423,1447,

%T 1597,1721,1783,1867,2237,2243,2999,3083,3119,3169,3229,3467,3673,

%U 3847,3853,3889,3943,4057,4091,4153,4219,4273,4519,4751,4787,5039,5119,5471,5573

%N Numbers the squares of which are in A231558.

%C Prime p is in the sequence, if and only if p, p^2, p^3, p^4, p^2+1 and p^2+p all are odious (A000069). We conjecture that the sequence contains also composite numbers, but the first one should be very large.

%H Peter J. C. Moses, <a href="/A231978/b231978.txt">Table of n, a(n) for n = 1..2500</a>

%F A230500((a(n)+1)/2)>=4.

%e 59^2=3481 is odious together with 59, 59^3=205379, 59^4=12117361, 59^2+1=3482 and 59^2 + 59=3540. Thus 59 is in the sequence.

%t odiousQ[n_]:=OddQ[DigitCount[n,2][[1]]]; selQ[n_]:=Apply[And,Map[odiousQ, Flatten[Map[{n+#,n*#,n/ #}&, Divisors[n]]]]]; Sqrt[Select[Range[3,5000]^2, (!PrimeQ[#]) && OddQ[#] && odiousQ[#] && selQ[#]&]] (* _Peter J. C. Moses_, Nov 16 2013 *)

%Y Cf. A000069, A231558.

%K nonn,base

%O 1,1

%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Nov 16 2013