The OEIS is supported by the many generous donors to the OEIS Foundation.

Numbers k such that k and k + 1 are both negabinary odious numbers.

2

`%I #11 Jan 29 2020 01:42:10
`

`%S 3,11,15,23,29,35,43,47,53,59,63,71,77,83,91,95,103,109,115,119,125,
`

`%T 131,139,143,151,157,163,171,175,181,187,191,199,205,211,215,221,227,
`

`%U 235,239,245,251,255,263,269,275,283,287,295,301,307,311,317,323,331,335
`

`%N Numbers k such that k and k + 1 are both negabinary odious numbers.
`

`%H Amiram Eldar, <a href="/A331831/b331831.txt">Table of n, a(n) for n = 1..10000</a>
`

`%e 3 is a term since both 3 and 3 + 1 = 4 are negabinary odious numbers (A268273): 3 has 3 digits of 1 in its negabinary representation, 111, 4 has 1 digit of 1 in its negabinary representation, 100, and both 3 and 1 are odd.
`

`%t negaBinWt[n_] := negaBinWt[n] = If[n==0, 0, negaBinWt[Quotient[n-1, -2]] + Mod[n, 2]]; odNegaBinQ[n_] := OddQ[negaBinWt[n]]; c = 0; k = 1; s = {}; v = Table[-1, {2}]; While[c < 60, If[odNegaBinQ[k], v = Join[Rest[v], {k}]; If[AllTrue[Differences[v], # == 1 &], c++; AppendTo[s, k - 1]]]; k++]; s
`

`%Y Cf. A157971, A268273, A331830.
`

`%K nonn,base
`

`%O 1,1
`

`%A _Amiram Eldar_, Jan 28 2020
`