A135061 a(n) = minimum (floor(n^3/m) + m) for any integer m >= 1.

2, 5, 10, 16, 22, 29, 37, 45, 54, 63, 72, 83, 93, 104, 116, 128, 140, 152, 165, 178, 192, 206, 220, 235, 250, 265, 280, 296, 312, 328, 345, 362, 379, 396, 414, 432, 450, 468, 487, 505, 525, 544, 563, 583, 603, 623, 644, 665, 686, 707, 728, 749, 771, 793, 815, 838, 860, 883, 906, 929, 952, 976, 1000

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Robert Israel, A135061(n) = floor(2 n^(3/2))

Formula

a(n) = floor(2*n^(3/2)), with the minimum occurring at m = ceiling(n^(3/2)). See link for proof. - Robert Israel, Mar 03 2017

Maple

f:= proc(n) local m, U, L;
U:= floor(2*n^(3/2));
m:=floor(n^(3/2));
L:= floor(min(n^3/m+m, n^3/(m+1)+m+1));
if L <> U then error("Conjecture fails") fi;
L
end proc:
map(f, [$1..100]); # Robert Israel, Mar 01 2017

Prog

(PARI) a(n)=local( minsum=0, cursum =0, minm=0, lastminsum=0); minsum = n^3 + 1; lastminsum= n^3 + 1; minm =1; for(m=1, n^3, cursum = floor(n^3/m + m); lastminsum = minsum; if(cursum < minsum, minsum = cursum); if(cursum < lastminsum, minm=m); ); print1("minm="minm" "); print1("minsum="minsum" ");

Crossrefs

Cf. A135072.

Sequence in context: A002134 A243971 A062472 * A323624 A348387 A086849

Adjacent sequences: A135058 A135059 A135060 * A135062 A135063 A135064

Keyword

nonn

Author

Alexander R. Povolotsky, Feb 11 2008, Feb 15 2008

Extensions

a(2) corrected and more terms added by Robert Israel, Mar 01 2017

Status

approved