A358798 a(1) = 2, a(2) = 3; for n > 2, a(n) is the smallest prime that can be appended to the sequence so that the smallest even number >= 4 that cannot be generated as the sum of two (not necessarily distinct) terms from {a(1), ..., a(n-1)} can be generated from {a(1), ..., a(n)}.

2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 29, 37, 41, 47, 43, 61, 53, 67, 59, 73, 71, 83, 89, 79, 97, 101, 103, 109, 107, 113, 127, 131, 139, 137, 149, 151, 163, 157, 179, 167, 173, 181, 193, 191, 211, 197, 199, 227, 233, 223, 229, 239, 251, 241, 277, 257, 271, 263

Offset

1,1

Comments

Related to the Goldbach conjecture. Proving that this sequence is non-terminating would prove the Goldbach conjecture.

Links

Travis J Weber, Table of n, a(n) for n = 1..10002

Travis J Weber, Python notebook code

Example

For n=5, the sequence a(1..4) is 2, 3, 5, 7. The even numbers 4..14 are sums of two terms and 16 is the smallest even number not a sum. The smallest prime allowing 16 to be made is 11, by 5 + 11 = 16. Thus, a(5) = 11.
For n=106, the smallest even number that is not the sum of two terms a(1..105) is 1082. The smallest prime allowing 1082 to be made is 541, by 541 + 541 = 1082. Thus, a(106) = 541.

Crossrefs

Sequence in context: A067903 A341934 A224229 * A102348 A161929 A216882

Adjacent sequences: A358795 A358796 A358797 * A358799 A358800 A358801

Keyword

nonn

Author

Travis J Weber, Dec 05 2022

Status

approved