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A110700 Number of zeros in the smallest prime with Hamming weight n (given by A061712). 5
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 (list; graph; refs; listen; history; text; internal format)
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: A101949 A124796 A065714 * A181875 A051908 A056614

Adjacent sequences:  A110697 A110698 A110699 * A110701 A110702 A110703

KEYWORD

nonn,base

AUTHOR

Max Alekseyev, Aug 03 2005

STATUS

approved

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Last modified April 21 20:59 EDT 2019. Contains 322328 sequences. (Running on oeis4.)