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A293764
Numbers k such that (d(k), d(k+1)) = (1,1) in the base-2 digits d(i) of sqrt(2).
4
3, 17, 18, 19, 23, 27, 31, 32, 33, 34, 35, 36, 40, 41, 44, 45, 46, 50, 68, 74, 75, 76, 77, 80, 88, 91, 95, 98, 99, 115, 116, 117, 118, 124, 125, 126, 127, 132, 133, 138, 141, 142, 143, 146, 155, 156, 171, 172, 175, 176, 189, 193, 194, 197, 206, 207, 208, 213
OFFSET
1,1
COMMENTS
This sequence together with A293761, A293762, and A293763 partition the positive integers.
LINKS
EXAMPLE
(d(i)) = (1,0,1,1,0,1,0,1,0,0,0,0,0,1,...) = A004539, in which (0,1) first occurs as (a(3),a(4)).
MATHEMATICA
z = 100; s = StringJoin[Map[ToString, First[RealDigits[N[Sqrt[2], 10000], 2]]]];
Take[Map[#[[1]]&, StringPosition[s, "00"]], z] (*A293761*)
Take[Map[#[[1]]&, StringPosition[s, "01"]], z] (*A293762*)
Take[Map[#[[1]]&, StringPosition[s, "10"]], z] (*A293763*)
Take[Map[#[[1]]&, StringPosition[s, "11"]], z] (*A293764*)
(* Peter J. C. Moses, Oct 15 2017 *)
SequencePosition[RealDigits[Sqrt[2], 2, 250][[1]], {1, 1}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 03 2019 *)
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Clark Kimberling, Oct 19 2017
STATUS
approved