A293764 - OEIS

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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).

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

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OFFSET

1,1

COMMENTS

This sequence together with A293761, A293762, and A293763 partition the positive integers.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

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*)