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A022776 Place where n-th 1 occurs in A023115. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 20 03:13 EDT 2019. Contains 328244 sequences. (Running on oeis4.)