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A110699 Binary length of the smallest prime with Hamming weight n (given by A061712). 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 13 19:25 EST 2018. Contains 317149 sequences. (Running on oeis4.)