A331463 Numbers k such that k and k + 1 are both binary hoax numbers (A329936).
8, 15, 49, 50, 252, 489, 699, 725, 755, 799, 951, 979, 980, 988, 989, 1023, 1134, 1350, 1351, 1370, 1390, 1599, 1629, 1630, 1660, 1690, 1694, 1763, 1854, 1908, 1929, 1939, 1940, 1960, 2006, 2015, 2166, 2312, 2358, 2645, 2700, 2779, 2787, 2862, 2923, 2930, 2988
Offset: 1
Examples
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.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Magma
hoax:=func
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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
Comments