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 A108421 Smallest number of ones needed to write in binary representation 2*n as sum of two primes. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS a(n) = Min{A000120(p)+A000120(q): p,q prime and p+q=2*n); a(n) = A108422(n) - A108423(n). a(n) >= A000120(n)+1, with equality for n in A241757. - Robert Israel, Mar 25 2018 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 EXAMPLE 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. 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 V[k] = 0 or t < V[k] then V[k]:= t fi od od: convert(V[2..N], list); # Robert Israel, Mar 25 2018 MATHEMATICA Min[#]&/@(Table[Total[Flatten[IntegerDigits[#, 2]]]&/@Select[ IntegerPartitions[ 2*n, {2}], AllTrue[#, PrimeQ]&], {n, 2, 110}]) (* Harvey P. Dale, Jul 27 2020 *) CROSSREFS Cf. A000120, A004676, A005843, A007088, A108422, A108423, A241757. Sequence in context: A162798 A088650 A097154 * A104058 A132345 A178976 Adjacent sequences: A108418 A108419 A108420 * A108422 A108423 A108424 KEYWORD nonn,base AUTHOR Reinhard Zumkeller, Jun 03 2005 STATUS approved

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Last modified July 22 06:32 EDT 2024. Contains 374481 sequences. (Running on oeis4.)