login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
LINKS
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 22:29 EDT 2024. Contains 370951 sequences. (Running on oeis4.)