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A331463 Numbers k such that k and k + 1 are both binary hoax numbers (A329936). 2
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 (list; graph; refs; listen; history; text; internal format)
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

Cf. A050219, A019506, A329935, A329936, A331464.

Sequence in context: A341117 A255428 A216443 * A151792 A243295 A118526

Adjacent sequences:  A331460 A331461 A331462 * A331464 A331465 A331466

KEYWORD

nonn,base

AUTHOR

Amiram Eldar, Jan 17 2020

STATUS

approved

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Last modified July 29 23:58 EDT 2021. Contains 346346 sequences. (Running on oeis4.)