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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A238459 Number of primes p < n with q(n-p) + 1 prime, where q(.) is the strict partition function (A000009). 3
0, 0, 1, 2, 2, 3, 2, 3, 3, 2, 3, 2, 5, 3, 5, 4, 4, 3, 4, 4, 6, 2, 4, 3, 5, 2, 4, 1, 4, 5, 6, 5, 5, 4, 5, 3, 4, 3, 5, 6, 5, 6, 3, 8, 6, 5, 6, 4, 6, 7, 5, 6, 4, 6, 7, 6, 7, 7, 6, 6, 7, 5, 6, 5, 6, 5, 5, 5, 7, 7, 6, 5, 7, 9, 8, 6, 5, 5, 7, 6, 8, 6, 5, 8, 7, 8, 7, 4, 8, 7, 7, 7, 6, 6, 6, 6, 6, 7, 6, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Conjecture: a(n) > 0 for all n > 2. Also, for each n > 6 there is a prime p < n with q(n-p) - 1 prime.

We have verified the conjecture for n up to 10^5.

See also A238458 for a similar conjecture involving the partition function p(n).

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014.

EXAMPLE

a(3) = 1 since 2 and q(3-2) + 1 = 1 + 1 = 2 are both prime.

a(28) = 1 since 17 and q(28-17) + 1 = q(11) + 1 = 12 + 1 = 13 are both prime.

MATHEMATICA

q[n_, k_]:=PrimeQ[PartitionsQ[n-Prime[k]]+1]

a[n_]:=Sum[If[q[n, k], 1, 0], {k, 1, PrimePi[n-1]}]

Table[a[n], {n, 1, 100}]

CROSSREFS

Cf. A000009, A000040, A237705, A237768, A237769, A238457, A238458.

Sequence in context: A080328 A245555 A031266 * A109301 A107573 A081308

Adjacent sequences:  A238456 A238457 A238458 * A238460 A238461 A238462

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Feb 27 2014

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 December 7 13:08 EST 2021. Contains 349581 sequences. (Running on oeis4.)