A159585 Nearest k to j such that k*(2^j-1)+1 is prime where j=A000043(n) and 2^j-1 = Mersenne-prime(n) = A000668(n). If there are two k values equidistant from j, each of which produces a prime, the larger of the two gets added to the sequence.
2, 4, 10, 4, 46, 22, 16, 46, 66, 136, 166, 124, 636, 550, 1474, 3066, 1656, 1816, 3708, 9436, 1746, 3696, 11262, 40138, 25900, 20808, 60340, 58818
Offset: 1
Examples
n=6, j=A000043(6)=17, A000668(6)=131071, then k=12 or k=22 are the nearest values to j which produce primes so we take the larger of the two k values for a(6)=22.