A383618 Smallest prime gap whose first occurrence is >= 2^n.

1, 4, 6, 6, 8, 8, 10, 16, 16, 16, 26, 30, 36, 38, 46, 46, 66, 74, 80, 94, 108, 116, 142, 156, 158, 166, 186, 200, 228, 254, 264, 294, 298, 334, 362, 388, 388, 422, 466, 488, 510, 536, 576, 590, 632, 676, 708, 764, 782, 796, 848, 926, 928, 968, 1006, 1048

Offset: 1

Author

Brian Kehrig, May 02 2025

Keywords

• nonn

Comments

In the case of a prime gap that straddles a power of 2, we take the lower end of the gap, as listed in A000230.

Examples

			a(3) = 6, because prime gaps of 1, 2, and 4 all appear before 2^3 = 8, but a prime gap of 6 does not occur until later.
		

Links

• Brian Kehrig, Table of n, a(n) for n = 1..65
• The Prime Gap List, First occurrence prime gaps

Crossrefs

Cf. A000230.