OFFSET
2,3
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.)
FORMULA
a(n) = 2*A151799(2*n - 1) - 2*n.
MATHEMATICA
Table[2 NextPrime[2 n - 1, -1] - 2 n, {n, 2, 100}]
PROG
(PARI) a(n) = 2*precprime(2*n-2) - 2*n; \\ Michel Marcus, May 10 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, May 10 2019
STATUS
approved