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%I #27 Sep 10 2019 21:40:52
%S 1,2,4,7,10,14,19,24,30,37,45,53,62,72,82,93,105,118,131,145,160,175,
%T 191,208,225,243,262,282,302,323,345,367,390,414,439,464,490,517,544,
%U 572,601,630,660,691,723,755,788,822,856,891,927,964,1001
%N Place where n-th 1 occurs in A023115.
%C Positions of the integers when the numbers a + b*sqrt(2) are arranged in increasing order. - _Clark Kimberling_, Mar 16 2015
%C It seems the name of this sequence could also be "Indices where records occur in A007336". - _Ivan N. Ianakiev_, Sep 09 2019
%H Clark Kimberling, <a href="/A022776/b022776.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = 1 + Sum_{k=1..n-1} ceiling(r*k) where r=1/sqrt(2). - _Benoit Cloitre_, Jan 24 2009
%e 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.
%t t = Table[n + 1 + Sum[Floor[(n - k)/Sqrt[2]], {k, 0, n}], {n, 0, 200}] (* A022776 *)
%t Differences[t] (* A049474 *) (* _Clark Kimberling_, Mar 14 2015 *)
%o (PARI) a(n)=1+sum(k=1,n-1,ceil(k/sqrt(2))) \\ _Benoit Cloitre_, Jan 24 2009
%Y Cf. A023115, A049474.
%K nonn
%O 1,2
%A _Clark Kimberling_
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