A333266 a(n) is the smallest number k such that for all m >= k there is at least one prime partition of m with prime(n) as least part.

4, 8, 15, 24, 39, 49, 67, 83, 89, 115, 127, 143, 163, 179, 193, 223, 235, 249, 271, 281, 295, 333, 349, 363, 387, 403, 409, 427, 461, 483, 515, 535, 545, 565, 595, 625, 643, 659, 685, 703, 725, 733, 759, 805, 813, 835, 851, 895, 907, 923, 937, 965, 989, 1033

Offset: 1

Author

David James Sycamore, Mar 13 2020

Keywords

• nonn

Comments

a(n) is a term if and only if it is the smallest number such that there exists a prime partition of every m in the interval [a(n), 2*a(n)] with least part prime(n). There is no prime partition of a(n)-1 having prime(n) as least part, and this is the greatest such number.

Examples

			For any k >= 4 there exists a prime partition of k having least part 2, hence a(1)=4.
		

Crossrefs

Cf. A333129, A333238, A330507, A000607, A333259.

Extensions

More terms from Alois P. Heinz, Mar 16 2020