A108421 -id:A108421 - cp's OEIS frontend

A108423 a(n) = A108422(n) - A108421(n).

0, 0, 0, 1, 0, 1, 0, 1, 2, 2, 1, 0, 1, 2, 0, 3, 2, 2, 2, 3, 3, 3, 1, 2, 2, 4, 1, 3, 3, 3, 0, 1, 0, 4, 3, 3, 4, 5, 2, 3, 4, 2, 3, 5, 4, 4, 1, 0, 4, 4, 3, 4, 4, 4, 2, 4, 2, 4, 3, 2, 1, 3, 0, 3, 2, 5, 4, 4, 5, 4, 3, 4, 4, 5, 3, 5, 5, 5, 2, 3, 4, 4, 4, 5, 3, 6, 1, 3, 5, 3, 1, 5, 4, 2, 1, 4, 4, 6, 4, 4, 4, 6, 2, 6, 4

Offset: 2

Reinhard Zumkeller, Jun 03 2005

a(A000079(n)) = 0.

Robert Israel, Table of n, a(n) for n = 2..10000

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):
VL:= Vector(N): VL[2]:= 2:
VH:= Vector(N): VH[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 > VH[k] then VH[k]:= t fi;
    if VL[k]=0 or t < VL[k] then VL[k]:= t fi;
  od
od:
convert((VH-VL)[2..N], list); # Robert Israel, Mar 26 2018

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

Original entry on oeis.org

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

Reinhard Zumkeller, Jun 03 2005

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

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

Cf. A004676, A005843, A007088, A108421.

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

cp's OEIS Frontend

A108423 a(n) = A108422(n) - A108421(n).

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