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

1,1

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.

Links

Table of n, a(n) for n=1..50.

Example

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.

Sequence in context: A079037 A281087 A101315 * A066541 A279728 A087122

Adjacent sequences: A343735 A343736 A343737 * A343739 A343740 A343741

Keyword

nonn

Author

Jon E. Schoenfield, Jun 27 2021

Status

approved