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A057768

From Goldbach problem: number of decompositions of 2n-1 into sum of a prime lucky number(from A031157) and a twin even-lucky-number(from A045955, A045956).

1 and 3 are not the sum of a prime lucky number and a twin even-lucky-number, so a(1) = a(2) = 0; 5=3+2 (one way, so a(3)=1); 7=3+4 (so a(4)=1); 9=3+6=7+2 (so a(5)=2); etc.