A110700 Number of zeros in the smallest prime with Hamming weight n (given by A061712).

1, 0, 0, 1, 0, 3, 0, 1, 1, 1, 1, 1, 0, 3, 1, 1, 0, 1, 0, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 0, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1

Offset

1,6

Comments

a(n)=0 iff n belongs A000043.

Observe that a(n)=3 for n=6, 14, 30, 62, 126, 254, 510, 1022, ... which is A000918. Conjecture: a(n) is never greater than 3. - T. D. Noe, Mar 14 2008

Links

T. D. Noe, Table of n, a(n) for n=1..1024

Formula

a(n) = A110699(n) - n.

Maple

with(combstruct); a:=proc(n) local m, is, s, t, r; if n=1 then return 1 fi; r:=+infinity; for m from 0 do is := iterstructs(Combination(n-2+m), size=n-2); while not finished(is) do s := nextstruct(is); t := 2^(n-1+m)+1+add(2^i, i=s); if isprime(t) then return m fi; od; od; return 0; end;

Mathematica

A061712[n_] := A061712[n] = Module[{m, s, k, p}, For[m=0, True, m++, s = {1, Sequence @@ #, 1} & /@ Permutations[Join[Table[1, {n - 2}], Table[0, {m}]]] // Sort; For[k=1, k <= Length[s], k++, p = FromDigits[s[[k]], 2]; If[PrimeQ[p], Return[p]]]]]; A061712[1]=2; Table[DigitCount[A061712[n], 2, 0], {n, 1, 100}] (* Jean-François Alcover, Mar 16 2015 *)

Crossrefs

Cf. A000043, A061712, A110699.

Sequence in context: A124796 A343858 A065714 * A375032 A338939 A292150

Adjacent sequences: A110697 A110698 A110699 * A110701 A110702 A110703

Keyword

nonn,base

Author

Max Alekseyev, Aug 03 2005

Status

approved