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A357128
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a(n) is the least even number k > 2 such that the sum of the lower elements and the sum of the upper elements in the Goldbach partitions of k are both divisible by 2^n, but not both divisible by 2^(n+1).
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0
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6, 4, 10, 16, 32, 468, 464, 3576, 14954, 96000, 403200
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OFFSET
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0,1
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COMMENTS
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LINKS
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EXAMPLE
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a(2) = 10 because the Goldbach partitions of 10 are 3+7 and 5+5, and 3+5 = 8 and 7+5 = 12 are both divisible by 2^2, but 12 is not divisible by 2^3; and 10 is the least even number > 2 that works.
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MAPLE
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N:= 10^4: # to use the first N primes
P:= [seq(ithprime(i), i=2..N)]:
M:= P[-1]+3:
L:= Vector(M): H:= Vector(M):
L[4]:= 2: H[4]:= 2:
for i from 1 to N-1 do
for j from i to N-1 do
t:= P[i]+P[j];
if t > M then break fi;
L[t]:= L[t]+P[i];
H[t]:= H[t]+P[j];
od od:
V:= Array(0..9): count:= 0:
for n from 4 by 2 to M while count < 10 do
v:= padic:-ordp(igcd(L[n], H[n]), 2);
if V[v]=0 then count:= count+1; V[v]:= n; fi
od:
convert(V, list);
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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