OFFSET
0,1
COMMENTS
EXAMPLE
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.
MAPLE
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);
CROSSREFS
KEYWORD
nonn,more
AUTHOR
J. M. Bergot and Robert Israel, Sep 13 2022
STATUS
approved