A072932 a(n) is the least k such that floor( (1+1/k)^n ) = floor( (1+1/n)^k ).

1, 2, 3, 4, 5, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66

Offset

1,2

Comments

If b(n) = abs( a(n) - 91n/100) then b(n) < 1/2 and sum(k=1,n,b(k)) is asymptotic to n/4.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Amiram Eldar, Plot of a(n)/n for n = 1..10000

Formula

a(n) is asymptotic to C*n with C a rational constant = 91/100; also a(100k)=91k.

Mathematica

a[n_] := Module[{k = 1}, While[Floor[(1+1/k)^n] != Floor[(1+1/n)^k], k++]; k]; Array[a, 100] (* Amiram Eldar, May 05 2022 *)

Prog

(PARI) a(n)=if(n<0, 0, s=1; while(abs(floor((1+1/n)^s)-floor((1+1/s)^n))>0, s++); s)

Crossrefs

Sequence in context: A319288 A106744 A332613 * A029915 A108141 A291811

Adjacent sequences: A072929 A072930 A072931 * A072933 A072934 A072935

Keyword

easy,nonn

Author

Benoit Cloitre, Aug 13 2002

Status

approved