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A328179 Number of distinct primes required to satisfy the Strong Goldbach Conjecture for all even numbers <= 2n. 1
0, 1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
The Strong Goldbach Conjecture asserts that all positive even integers >=4 can be expressed as the sum of two primes.
If the Strong Goldbach Conjecture is true, then a(n) > 0 for all n > 1 and a(n) <= a(n+1) for all n.
LINKS
EXAMPLE
a(1)=0 because 2 does not have any Goldbach partition.
a(2)=1 because 4=2+2 and 2 is the only prime required for all even numbers <= 4.
a(3)=2 because 4=2+2 and 6=3+3, thus 2 and 3 are required for expressing all even numbers <= 6.
a(7)=4 because using {2,3,5,7} it is possible to build all even numbers <= 14.
a(8)=5 because using either {2,3,5,7,11} or {2,3,5,7,13} it is possible to build all even numbers <= 16.
a(10)=5 because {2,3,5,7,13} are enough to build all even numbers <= 20.
CROSSREFS
Sequence in context: A132663 A306631 A023964 * A000267 A249728 A060020
KEYWORD
nonn
AUTHOR
Marcin Barylski, Oct 06 2019
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)