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 A231978 Numbers the squares of which are in A231558. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 3 18:44 EDT 2023. Contains 363116 sequences. (Running on oeis4.)