A103341 Numbers k such that floor(k*sqrt(2)) is a power of 2.

1, 2, 3, 6, 12, 23, 91, 2897, 5793, 23171, 46341, 92682, 185364, 370728, 1482911, 2965821, 5931642, 23726567, 47453133, 94906266, 379625063, 759250125, 1518500250, 3037000500, 6074001000, 12148002000, 24296004000, 48592008000

Offset

1,2

Comments

Sequence is infinite.

If floor(sqrt(2)*2^k) + 1 < sqrt(2)*2^k + sqrt(2)/2, then floor(sqrt(2)*2^k) + 1 is in this sequence. - Jinyuan Wang, Nov 04 2018

References

Jean-Marie De Koninck and Armel Mercier, 1001 problèmes en théorie classique des nombres, ellipses, 2004, pp. 117, 374-375.

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Maple

N:= 100: # to get a(1)..a(N)
count:= 0:
for k from 0 while count < N do
  a:= ceil(2^(k-1)*sqrt(2));
  b:= floor((2^(k-1)+1/2)*sqrt(2));
  if a=b then
     count:= count+1;
     A[count]:= a;
  fi
od:
seq(A[n], n=1..N); # Robert Israel, Jul 19 2016

Mathematica

f[k_] := Reduce[n > 0 && (2^k)^2<= 2*n^2 <  (2^k + 1)^2, n, Integers]; n /. ToRules /@ Select[Table[f[k], {k, 0, 40}], # =!= False & ] (* Jean-François Alcover, Sep 13 2011 *)

Prog

(PARI) for(k=0, 50, n=ceil(2^k/sqrt(2)); if(floor(n*sqrt(2))==2^k, print1(n, ", "))) \\ Robert Gerbicz, Jun 09 2007
(PARI) isok(n) = my(b=sqrtint(2*n^2)); (b==1) || (b==2) || (isprimepower(b, &p) && (p==2); \\ Michel Marcus, Mar 12 2019
(Magma) [n: n in [1..2*10^7] | 2^Ilog(2, s) eq s where s is Floor(n*Sqrt(2))]; // Vincenzo Librandi, Nov 06 2018

Crossrefs

Cf. A001951 (floor(n*sqrt(2))).

Sequence in context: A326021 A164363 A306809 * A023675 A029996 A294123

Adjacent sequences: A103338 A103339 A103340 * A103342 A103343 A103344

Keyword

nonn

Author

Benoit Cloitre, May 13 2007

Extensions

More terms from Robert Gerbicz, Jun 09 2007

Status

approved