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

Author

Ralf Stephan, May 18 2003

Keywords

• nonn
• base

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A084186.

Programs

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 *)