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A331463 Numbers k such that k and k + 1 are both binary hoax numbers (A329936).

%I A331463 #13 Sep 08 2022 08:46:25
%S A331463 8,15,49,50,252,489,699,725,755,799,951,979,980,988,989,1023,1134,
%T A331463 1350,1351,1370,1390,1599,1629,1630,1660,1690,1694,1763,1854,1908,
%U A331463 1929,1939,1940,1960,2006,2015,2166,2312,2358,2645,2700,2779,2787,2862,2923,2930,2988
%N A331463 Numbers k such that k and k + 1 are both binary hoax numbers (A329936).
%H A331463 Amiram Eldar, <a href="/A331463/b331463.txt">Table of n, a(n) for n = 1..10000</a>
%e A331463 8 is a term since both 8 and 8 + 1 = 9 are binary hoax numbers: 8 = 2^3 in binary representation is 1000 = 10^3 and 1 + 0 + 0 + 0 = 1 + 0, and 9 = 3^2 in binary representation is 1001 = 11^2 and 1 + 0 + 0 + 1 = 1 + 1.
%t A331463 binWt[n_] := Total @ IntegerDigits[n, 2]; binHoaxQ[n_] := CompositeQ[n] && Total[binWt /@ FactorInteger[n][[;; , 1]]] == binWt[n]; seq = {}; isHoax1 = binHoaxQ[1]; Do[isHoax2 = binHoaxQ[n]; If[isHoax1 && isHoax2, AppendTo[seq, n-1]]; isHoax1 = isHoax2, {n, 2, 3000}]; seq
%o A331463 (Magma) hoax:=func<n| not IsPrime(n) and (&+Intseq(n,2) eq &+[ &+Intseq(p,2): p in PrimeDivisors(n)])>; [k:k in [2..3000]|hoax(k) and hoax(k+1)]; // _Marius A. Burtea_, Jan 17 2020
%Y A331463 Cf. A050219, A019506, A329935, A329936, A331464.
%K A331463 nonn,base
%O A331463 1,1
%A A331463 _Amiram Eldar_, Jan 17 2020