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URL: https://oeis.org/A233327

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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
OFFSET
0,4
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
Bisections: a(2n) = abs(A238455(n)), a(2n+1) = A000079(n).
Sequence in context: A117000 A082392 A377377 * A307107 A085086 A274623
KEYWORD
nonn,easy
AUTHOR
Alex Ratushnyak, Feb 23 2014
STATUS
approved