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COMMENT
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Expression 2^j+q^j below q=prime<=prime[130] provided always prime at j=0; or for j=1 if q is a lesser-twin-prime; or more rarely 3 or 4 primes [four ones at q=3,5,17,37,59,137,179,223,461]; never found 5 or more relevant primes and the corresponding exponents proved to be powers of 2. Formal proofs of observations wanted.
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EXAMPLE
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The relevant exponents are powers of 2: 0,4,8,128
a[4]=2^128+223^128 = a-prime-with-301-decimal-digits = 382844.....1067137.
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