OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
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.
MATHEMATICA
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
PROG
(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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Jan 17 2020
STATUS
approved