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

1,2

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

Links

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

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A023115, A049474.

Sequence in context: A022339 A025711 A117634 * A025704 A025710 A023536

Adjacent sequences: A022773 A022774 A022775 * A022777 A022778 A022779

Keyword

nonn

Author

Clark Kimberling

Status

approved