A343738 a(n) is the smallest prime p > k such that p + k is a power of 2, where k = 2*n - 1, or 0 if no such prime exists.

3, 5, 11, 549755813881, 23, 53, 19, 17, 47, 109, 43, 41, 103, 37, 227, 97, 223, 16349, 2011, 89, 983, 536870869, 83, 977, 79, 461, 971, 73, 71, 197, 67, 193, 191, 524221, 443, 953, 439, 181, 179, 433, 431, 173, 130987, 937, 167, 421, 163, 929, 1951, 157

Offset: 1

Author

Jon E. Schoenfield, Jun 27 2021

Keywords

• nonn

Comments

k = 2*n-1 is the n-th odd number; p is the smallest prime > k such that p+k is a power of 2. If the constraint "> k" were removed, sequence A096822 would result.

Examples

			For n=1, k = 2*n-1 = 1, and the smallest prime p > 1 such that p+1 is a power of 2 is 3, so a(1)=3.
For n=3, k=5, and the smallest prime p > 5 such that p+5 is a power of 2 is 11, so a(3)=11.
For n=4, k=7, and there is no prime in the sequence {2^4 - 7 = 9, 2^5 - 7 = 25, 2^6 - 7 = 57, ...} until 2^39 - 7 = 549755813881, so a(4) = 549755813881.
For n=55, k=109, and the smallest prime p > 109 such that p+109 is a prime is a(55) = 2^963 - 109 (a 290-digit number).
		

Crossrefs

Cf. A096822.