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A294108
Minimum of the number of primes appearing among the smaller parts and the number of primes appearing among the larger parts of the partitions of n into two parts.
1
0, 0, 0, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 3, 3, 4, 4, 4, 3, 4, 4, 4, 3, 3, 3, 4, 4, 5, 5, 5, 4, 4, 4, 5, 4, 4, 4, 5, 5, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 6, 7, 7, 8, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 9, 9, 9, 9, 9, 10, 10, 10, 9, 10
OFFSET
1,6
FORMULA
a(n) = min(Sum_{i=1..floor(n/2)} A010051(i), Sum_{i=1..floor(n/2)} A010051(n-i)).
EXAMPLE
a(14) = 3; the partitions of 14 into two parts are 13+1, 12+2, 11+3, 10+4, 9+5, 8+6, 7+7. There are three primes among the larger parts and four primes among the smaller parts, so min(3,4) = 3. - Wesley Ivan Hurt, Nov 18 2017
MATHEMATICA
Table[Min[Sum[PrimePi[i] - PrimePi[i - 1], {i, Floor[n/2]}], Sum[PrimePi[n - i] - PrimePi[n - i - 1], {i, Floor[n/2]}]], {n, 80}]
PROG
(PARI) a(n) = min(sum(i=1, n\2, isprime(i)), sum(i=1, n\2, isprime(n-i))); \\ Michel Marcus, Nov 19 2017
CROSSREFS
Sequence in context: A043530 A297771 A164995 * A055718 A007302 A362028
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 22 2017
STATUS
approved