A084185 First occurrence of binary n in the binary expansion of sqrt(2).

1, 1, 3, 8, 1, 3, 17, 8, 14, 4, 1, 19, 3, 18, 17, 8, 62, 51, 14, 6, 4, 1, 42, 80, 19, 3, 41, 18, 40, 17, 31, 8, 57, 62, 128, 51, 69, 20, 14, 6, 104, 4, 111, 66, 1, 96, 42, 146, 80, 50, 19, 118, 3, 77, 41, 126, 18, 98, 40, 17, 75, 33, 31, 453, 8, 57

Offset

1,3

Comments

a(n)=1 iff n in A084188. a(2^(n+1)+1) = A084187(n)-1.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Example

The binary expansion of sqrt(2) is 1.0110101000001..(A004539) and binary(10)=1010 occurs first at index 4, so a(10)=4.

Mathematica

With[{s2=RealDigits[Sqrt[2], 2, 1000][[1]], n2=IntegerDigits[n, 2]}, Flatten[ Table[First[ Position[Partition[s2, Length[n2], 1], n2]], {n, 70}]]] (* Harvey P. Dale, Oct 11 2012 *)

Crossrefs

Cf. A084186.

Sequence in context: A210962 A021728 A242710 * A073227 A016550 A238169

Adjacent sequences: A084182 A084183 A084184 * A084186 A084187 A084188

Keyword

nonn,base

Author

Ralf Stephan, May 18 2003

Status

approved