A397306 - OEIS

A397306

Positive numbers m such that m - 2^k is a prime for exactly one value of k > 0 with 2^k < m.

4, 5, 6, 10, 17, 18, 29, 34, 41, 53, 59, 65, 66, 89, 97, 119, 130, 137, 163, 179, 185, 191, 193, 209, 217, 219, 221, 223, 233, 239, 247, 253, 258, 269, 281, 305, 307, 311, 343, 359, 389, 403, 407, 415, 419, 427, 431, 457, 491, 505, 514, 521, 533, 545, 547, 557, 569, 575, 581

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OFFSET

1,1

COMMENTS

With r(m) = #{k > 0 : 2^k < m, m-2^k is prime}, this sequence gives terms satisfying r(m) = 1.

When m is even, then m-2^k is even for all k>0; as the only even prime is 2, necessarily, subsequence of even terms correspond to A052548 \ {3}.

Subsequence of odd terms is A283806 \ {3} (see example section).

LINKS

Table of n, a(n) for n=1..59.

FORMULA

Equals (Union of A052548 and A283806) \ {3}.

EXAMPLE