A231978 Numbers the squares of which are in A231558.

59, 103, 193, 229, 251, 313, 431, 761, 929, 1019, 1087, 1279, 1367, 1423, 1447, 1597, 1721, 1783, 1867, 2237, 2243, 2999, 3083, 3119, 3169, 3229, 3467, 3673, 3847, 3853, 3889, 3943, 4057, 4091, 4153, 4219, 4273, 4519, 4751, 4787, 5039, 5119, 5471, 5573

Offset

1,1

Comments

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.

Links

Peter J. C. Moses, Table of n, a(n) for n = 1..2500

Formula

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

Example

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.

Mathematica

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 *)

Crossrefs

Cf. A000069, A231558.

Sequence in context: A106869 A147092 A142298 * A180947 A060259 A141934

Adjacent sequences: A231975 A231976 A231977 * A231979 A231980 A231981

Keyword

nonn,base

Author

Vladimir Shevelev and Peter J. C. Moses, Nov 16 2013

Status

approved