login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A295630 Number of partitions of n into two distinct parts that are not both prime. 0
0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 5, 4, 5, 5, 6, 5, 8, 6, 8, 7, 9, 8, 11, 8, 11, 10, 13, 11, 14, 11, 14, 13, 15, 13, 17, 13, 18, 17, 18, 16, 20, 16, 20, 18, 21, 19, 23, 18, 23, 20, 25, 22, 26, 21, 26, 24, 28, 25, 29, 23, 29, 28, 30, 26, 32, 26, 33, 31, 33, 29 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..70.

Index entries for sequences related to Goldbach conjecture

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{i=1..floor((n-1)/2)} 1 - A010051(i)*A010051(n-i).

EXAMPLE

a(12) = 4; The partitions of 12 into two distinct parts are (11,1), (10,2), (9,3), (8,4) and (7,5). Of these partitions, the parts in (11,1), (10,2), (9,3) and (8,4) are not both prime, so a(12) = 4.

MATHEMATICA

Table[Sum[1 - (PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i] - PrimePi[n - i - 1]), {i, Floor[(n - 1)/2]}], {n, 80}]

CROSSREFS

Cf. A010051, A295629.

Sequence in context: A248972 A077563 A055256 * A029147 A228571 A224908

Adjacent sequences:  A295627 A295628 A295629 * A295631 A295632 A295633

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Nov 24 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 30 05:03 EDT 2020. Contains 337435 sequences. (Running on oeis4.)