A108422 Greatest number of ones that can be used to write in binary representation 2*n as sum of two primes.

2, 4, 4, 5, 5, 6, 5, 6, 6, 6, 6, 6, 6, 7, 6, 7, 7, 8, 7, 8, 8, 8, 7, 8, 8, 9, 7, 8, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 8, 9, 10, 10, 10, 8, 8, 9, 9, 9, 10, 10, 10, 9, 9, 8, 10, 10, 10, 8, 10, 8, 9, 9, 10, 9, 10, 10, 9, 9, 10, 9, 11, 9, 10, 11, 12, 9, 10, 10, 10, 10, 11, 9, 12, 8, 9, 11, 10, 8, 12

Offset: 2

Author

Reinhard Zumkeller, Jun 03 2005

Keywords

• nonn
• base

Comments

a(n) = Max{A000120(p)+A000120(q) : p,q prime and p+q=2*n}.

a(n) = A108423(n) + A108421(n).

Links

• Robert Israel, Table of n, a(n) for n = 2..10000
• Index entries for sequences related to Goldbach conjecture
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A004676, A005843, A007088, A108421.

Programs

Maple

N:= 200: # to get a(2)..a(N)
Primes:= select(isprime, [seq(i, i=3..2*N-3, 2)]):
Ones:= map(t -> convert(convert(t, base, 2), `+`), Primes):
V:= Vector(N): V[2]:= 2:
for i from 1 to nops(Primes) do
  p:= Primes[i];
  for j from 1 to i do
    k:= (p+Primes[j])/2;
    if k > N then break fi;
    t:= Ones[i]+Ones[j];
    if t > V[k] then V[k]:= t fi
  od
od:
convert(V[2..N], list); # Robert Israel, Mar 26 2018