A108422 - OEIS

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A108422

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

3

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

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OFFSET

2,1

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

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

CROSSREFS

Cf. A004676, A005843, A007088, A108421.

Sequence in context: A036443 A036437 A053306 * A276523 A244320 A084616

Adjacent sequences: A108419 A108420 A108421 * A108423 A108424 A108425

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Jun 03 2005

STATUS

approved