The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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)}. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 4 18:39 EST 2023. Contains 367563 sequences. (Running on oeis4.)