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

Author

Max Alekseyev, Aug 03 2005

Keywords

• nonn
• base

Comments

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

Links

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

Crossrefs

Cf. A000043, A061712, A110700.

Programs

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 *)

PARI

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

Formula

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