|
|
A233327
|
|
Distance from 2^n to the nearest triangular number.
|
|
3
|
|
|
0, 1, 1, 2, 1, 4, 2, 8, 3, 16, 11, 32, 1, 64, 87, 128, 167, 256, 306, 512, 500, 1024, 552, 2048, 688, 4096, 3041, 8192, 579, 16384, 20854, 32768, 37075, 65536, 55618, 131072, 37108, 262144, 222296, 524288, 147729, 1048576, 891994, 2097152, 602155, 4194304, 3523022
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
LINKS
|
|
|
FORMULA
|
a(2*k+1) = 2^k.
Specifically, both the nearest triangular number below: A006516(n) = A000217((2^n)-1) = 2^(2n-1) - 2^(n-1) and the nearest triangular number above: A007582(n) = A000217(2^n) = 2^(2n-1) + 2^(n-1) are at the same distance from 2^(2n-1). - Antti Karttunen, Feb 26 2014
|
|
EXAMPLE
|
Triangular number nearest to 2^8=256 is 253, so a(8)=256-253=3.
|
|
MATHEMATICA
|
a[n_] := Module[{k, k0}, k0 = k /. FindRoot[2^n == k*(k+1)/2, {k, 2^(n/2)}, WorkingPrecision -> 20] // Round; Abs[2^n-k0*(k0+1)/2]]; Table[a[n], {n, 0, 46}] (* Jean-François Alcover, Feb 27 2014 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|