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A083201
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a(1) = 1. For n>1, let x = a(n-1)+1; then a(n) is the first prime in the sequence 2*x-1, 2*x-3, 4*x-1, 4*x-3, 8*x-1, 8*x-3, ..., (2^k)*x-1, (2^k)*x-3, ...
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1
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1, 3, 7, 13, 53, 107, 431, 863, 6911, 27647, 442367, 7247757311, 3710851743743, 7421703487487, 31875973759370105192447, 71778311772385457136805581255138607103
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