A055065 Smallest even number that is the sum of distinct primes in exactly n ways.

8, 16, 24, 36, 48, 60, 78, 84, 90, 114, 144, 120, 168, 180, 234, 246, 288, 240, 210, 324, 300, 360, 474, 330, 528, 576, 390, 462, 480, 420, 570, 510, 672, 792, 756, 876, 714, 798, 690, 1038, 630, 1008, 930, 780, 960, 870, 924, 900, 1134, 1434, 840, 990

Offset

1,1

Comments

Proposed by G. L. Honaker, Jr.

Essentially a greedy inverse of A061357: a(n)/2 is the index of the first appearance of n in A061357. - R. J. Mathar, Jul 10 2026

Links

R. J. Mathar, Table of n, a(n) for n = 1..382

Formula

a(n) >= A087747(n). - R. J. Mathar, Jul 10 2026

Example

16 is the sum of distinct primes in exactly 2 ways (3 + 13 and 5 + 11), and is the smallest such number, so a(2) = 16.

Maple

A055065 := proc(n)
    local a, p, q, N, i ;
    for a from 2 by 2 do
        N := 0 ;
        for i from 1 do
            p := ithprime(i) ;
            q := a-p ;
            if q < p then
                break ;
            end if;
            if isprime(q) and p <> q then
                N := N+1 ;
            end if;
        end do:
        if N = n then
            return a ;
        end if;
    end do:
end proc:
seq(A055065(n), n=1..60) ; # R. J. Mathar, Jul 10 2026

Crossrefs

Cf. A001172.

Sequence in context: A072066 A342018 A369035 * A181311 A083496 A125991

Adjacent sequences: A055062 A055063 A055064 * A055066 A055067 A055068

Keyword

nonn

Author

Jud McCranie, Jun 12 2000

Status

approved