A022776 Place where n-th 1 occurs in A023115.

1, 2, 4, 7, 10, 14, 19, 24, 30, 37, 45, 53, 62, 72, 82, 93, 105, 118, 131, 145, 160, 175, 191, 208, 225, 243, 262, 282, 302, 323, 345, 367, 390, 414, 439, 464, 490, 517, 544, 572, 601, 630, 660, 691, 723, 755, 788, 822, 856, 891, 927, 964, 1001

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

Positions of the integers when the numbers a + b*sqrt(2) are arranged in increasing order. - Clark Kimberling, Mar 16 2015

It seems the name of this sequence could also be "Indices where records occur in A007336". - Ivan N. Ianakiev, Sep 09 2019

Examples

			The ordering of numbers a+b*r, where r = sqrt(2) as in Comments, begins with 0, 1, r, 2, 1+r, 2r, 3, 2+r, 1+2r, 4, ... in which the positions of integers are 1, 2, 4, 7, 10.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A023115, A049474.

Programs

Mathematica

t = Table[n + 1 + Sum[Floor[(n - k)/Sqrt[2]], {k, 0, n}], {n, 0, 200}] (* A022776 *)
Differences[t] (* A049474 *) (* Clark Kimberling, Mar 14 2015 *)

PARI

a(n)=1+sum(k=1,n-1,ceil(k/sqrt(2))) \\ Benoit Cloitre, Jan 24 2009

Formula

a(n) = 1 + Sum_{k=1..n-1} ceiling(r*k) where r=1/sqrt(2). - Benoit Cloitre, Jan 24 2009