A331831 Numbers k such that k and k + 1 are both negabinary odious numbers.
3, 11, 15, 23, 29, 35, 43, 47, 53, 59, 63, 71, 77, 83, 91, 95, 103, 109, 115, 119, 125, 131, 139, 143, 151, 157, 163, 171, 175, 181, 187, 191, 199, 205, 211, 215, 221, 227, 235, 239, 245, 251, 255, 263, 269, 275, 283, 287, 295, 301, 307, 311, 317, 323, 331, 335
Offset: 1
Examples
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.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
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