A110699 Binary length of the smallest prime with Hamming weight n (given by A061712).

2, 2, 3, 5, 5, 9, 7, 9, 10, 11, 12, 13, 13, 17, 16, 17, 17, 19, 19, 21, 22, 24, 24, 25, 26, 28, 28, 29, 30, 33, 31, 33, 34, 35, 36, 38, 38, 40, 40, 41, 42, 44, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 56, 57, 59, 59, 60, 61, 61, 65, 64, 65, 66, 67, 68, 69, 70, 72, 72, 73

Offset

1,1

Comments

a(n)=n iff n belongs to A000043.

Links

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

Formula

a(n) = n + A110700(n).

Maple

with(combstruct); a:=proc(n) local m, is, s, t, r; if n=1 then return 2 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 n+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[IntegerDigits[A061712[n], 2] // Length, {n, 1, 100}] (* Jean-François Alcover, Mar 16 2015 *)

Prog

(PARI) a(n) = {forprime(p=2, , if (hammingweight(p) == n, return(#binary(p))); ); } \\ Michel Marcus, Mar 16 2015

Crossrefs

Cf. A000043, A061712, A110700.

Sequence in context: A280470 A011971 A060048 * A035537 A285407 A292802

Adjacent sequences: A110696 A110697 A110698 * A110700 A110701 A110702

Keyword

nonn,base

Author

Max Alekseyev, Aug 03 2005

Status

approved