A380978 Sequence of minimal Fermat witnesses for compositeness. a(n) is the least k such that the smallest composite number that is a Fermat pseudoprime to bases {a(i) : 1 <= i < n} is not a Fermat pseudoprime to base k.

2, 3, 5, 7, 13, 11, 17, 41, 37, 19, 31, 43, 23, 53, 29, 101, 61, 109, 71, 67, 73, 113, 151, 89, 97, 211, 191, 157, 163, 193, 139, 281, 107, 103, 181, 47, 127, 271, 131, 307, 59, 257, 229, 331, 337, 199, 241, 461, 239, 617, 367, 263, 401, 251, 149, 421, 137, 277

Offset: 1

Author

Jan Kostanjevec, Feb 10 2025

Keywords

• nonn

Examples

			For n = 1, a(1) = 2, since 2 is the first Fermat witness, proving the compositeness of 4.
For n = 2, a(2) = 3, since 3 is the next required Fermat witness, proving the compositeness of 341 (all previous composites are witnessed by 2).
For n = 3, a(3) = 5, since 5 is the next required Fermat witness, proving the compositeness of  1105 (all previous composites are witnessed by 2 and 3).
		

Links

• Eric Weisstein's World of Mathematics, Fermat Pseudoprime, Witness
• Index entries for sequences related to pseudoprimes

Crossrefs

Cf. A001567, A089105, A321790, A380979.

Formula

a(1) = 2, otherwise a(n) = A321790(k), where k is such that A001567(k) = A380979(n). - Peter Munn, Mar 12 2025

Extensions

More terms from Jinyuan Wang, Mar 05 2025