A261153 a(n) is the maximum number of distinct primes whose sum is n.

0, 0, 1, 1, 0, 2, 0, 2, 2, 2, 3, 1, 3, 2, 3, 3, 3, 4, 3, 3, 3, 4, 3, 4, 3, 4, 4, 4, 5, 4, 5, 4, 4, 4, 5, 4, 5, 4, 5, 5, 5, 6, 5, 5, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 6, 6, 7

Offset

0,6

Comments

a(A007504(k)) = k.

a(n) < k when n < A007504(k).

Let pi(j) be the j-th prime. Then a(A007504(k) - pi(j)) = k-1, j<=k. For example, k=5: A007504(5) = 28, pi(5)=11. So a(n)=4, n = {26,25,23,21,17}.

Similarly, a(A007504(k) + pi(j)) = k+1, where j>k and A007504(k) + pi(j) < A007504(k+2). For example, k=8: A007504(8) = 77, A007504(10) = 129 and pi(8)=19. Therefore, a(n)=9, n = {100,106,108,114,118,120,124}.

Links

Table of n, a(n) for n=0..58.

Example

a(26)=4 because 3+5+7+11 = 26. Note that some terms may be expressed in multiple ways. For example, a(47)=6: 2+3+5+7+11+19 and 2+3+5+7+13+17 = 47.

Crossrefs

Cf. A000040 (prime numbers), A007504.

Sequence in context: A278248 A036461 A244478 * A199123 A325589 A291308

Adjacent sequences: A261150 A261151 A261152 * A261154 A261155 A261156

Keyword

nonn,easy

Author

Bob Selcoe, Aug 10 2015

Status

approved