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A108421
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Smallest number of ones needed to write in binary representation 2*n as sum of two primes.
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3
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2, 4, 4, 4, 5, 5, 5, 5, 4, 4, 5, 6, 5, 5, 6, 4, 5, 6, 5, 5, 5, 5, 6, 6, 6, 5, 6, 5, 6, 7, 7, 7, 8, 5, 5, 6, 5, 5, 6, 6, 5, 6, 6, 5, 6, 6, 7, 8, 5, 5, 6, 6, 6, 6, 7, 5, 6, 6, 7, 8, 7, 7, 8, 6, 7, 5, 5, 6, 5, 5, 6, 6, 5, 6, 6, 5, 6, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 7, 7, 7, 8, 7, 8, 6, 5, 5, 6, 6, 6, 6, 7, 5, 6
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OFFSET
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2,1
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COMMENTS
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LINKS
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EXAMPLE
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n=15: 2*15=30 and A002375(15)=3 with 30=7+23=11+19=13+17,
13+17 -> 1101+10001 needs a(15)=5 binary ones, whereas
7+23 -> 111+10111 and 11+19 -> 1011+10011 need more.
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MAPLE
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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 V[k] = 0 or t < V[k] then V[k]:= t fi
od
od:
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MATHEMATICA
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Min[#]&/@(Table[Total[Flatten[IntegerDigits[#, 2]]]&/@Select[ IntegerPartitions[ 2*n, {2}], AllTrue[#, PrimeQ]&], {n, 2, 110}]) (* Harvey P. Dale, Jul 27 2020 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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