A308044 a(n) = 2*prevprime(2*n-1) - 2*n, where prevprime(n) is the largest prime < n.

0, 0, 2, 4, 2, 8, 10, 8, 14, 16, 14, 20, 18, 16, 26, 28, 26, 24, 34, 32, 38, 40, 38, 44, 42, 40, 50, 48, 46, 56, 58, 56, 54, 64, 62, 68, 70, 68, 66, 76, 74, 80, 78, 76, 86, 84, 82, 80, 94, 92, 98, 100, 98, 104, 106, 104, 110, 108, 106, 104, 102, 100, 98, 124

Offset: 2

Author

Wesley Ivan Hurt, May 10 2019

Keywords

• nonn
• easy

Comments

a(n) is the difference between the parts in the single partition of 2*n into two parts such that the larger part is the biggest prime < 2*n - 1.

For n > 1, the sequence of terms agrees with A303603 up to a(48), but a(49) = 80, whereas A303603(49) = 60. (This is because the smallest prime less than 2*49 - 1 = 97 is 89, which is paired with 9. This is the first instance in which the largest prime < 2*n - 1 is not paired with a prime. Regardless of whether the smallest part is prime or composite, we take the difference. So a(49) = 89 - 9 = 80.)

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A151799, A303603.

Programs

Mathematica

Table[2 NextPrime[2 n - 1, -1] - 2 n, {n, 2, 100}]

PARI

a(n) = 2*precprime(2*n-2) - 2*n; \\ Michel Marcus, May 10 2019

Formula

a(n) = 2*A151799(2*n - 1) - 2*n.