A062091 a(1) = 2, a(n)= smallest even number which does not divide the product of all previous terms.

2, 4, 6, 10, 14, 18, 22, 26, 34, 38, 46, 50, 58, 62, 74, 82, 86, 94, 98, 106, 118, 122, 134, 142, 146, 158, 162, 166, 178, 194, 202, 206, 214, 218, 226, 242, 254, 262, 274, 278, 298, 302, 314, 326, 334, 338, 346, 358, 362, 382, 386, 394, 398, 422, 446, 454

Offset: 1

Author

Amarnath Murthy, Jun 16 2001

Keywords

• nonn

Examples

			After 10 the next term in the sequence is 14 (not 12) as 12 = 2*6 divides the product of all the previous terms.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A026477, A062090.

Programs

Mathematica

Block[{a = {2}, k = 4, P = 1}, Do[Set[P, P*a[[-1]]]; While[Mod[P, k] == 0, k += 2]; AppendTo[a, k], {i, 2, 56}]; a] (* Michael De Vlieger, Nov 04 2020 *)

Formula

2 and 4 together with numbers of the form 2*{p^(2^k)} where p is an odd prime and k is a nonnegative integer. [Corrected by Peter Munn, Nov 03 2020]

Conjecture: a(n) = 2*A062090(n-1) for n>=3. - R. J. Mathar, Jul 08 2025

Extensions

More terms from Dean Hickerson, Jul 10 2001