A182765 Beatty sequence for (6 + sqrt(2))/4.

1, 3, 5, 7, 9, 11, 12, 14, 16, 18, 20, 22, 24, 25, 27, 29, 31, 33, 35, 37, 38, 40, 42, 44, 46, 48, 50, 51, 53, 55, 57, 59, 61, 63, 64, 66, 68, 70, 72, 74, 75, 77, 79, 81, 83, 85, 87, 88, 90, 92, 94, 96, 98, 100, 101, 103, 105, 107, 109, 111, 113, 114, 116, 118, 120, 122, 124, 126, 127

Offset: 1

Author

Clark Kimberling, Nov 29 2010

Keywords

• nonn

Comments

Let u=(1+sqrt(2))/2 and v=sqrt(2). Jointly rank {ju} and {kv} as in the first comment at A182760; a(n) is the position of nu.

Crossrefs

Cf. A182766.

Programs

Mathematica

Table[Floor[(6 + Sqrt@ 2) n/4], {n, 70}] (* Michael De Vlieger, Jun 23 2016 *)

PARI

A182765(n)=n*(6+sqrt(2))\4 \\ Requires sufficient realprecision (but the 64-bit default is enough up to n = 10^38). - M. F. Hasler, Jun 23 2016

Formula

a(n) = floor(r*n), where r = (6 + sqrt(2))/4.

a(n) = 2*n - 1 - floor(n/7) for n < 41, but this fails for a(41) = 75 onwards. - M. F. Hasler, Jun 23 2016