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

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!)
 A238646 Number of primes p < n such that the number of squarefree numbers among 1, ..., n-p is prime. 2
 0, 0, 0, 1, 2, 2, 2, 2, 3, 1, 2, 1, 3, 1, 3, 1, 4, 2, 3, 2, 5, 4, 5, 1, 3, 3, 4, 2, 5, 3, 4, 5, 8, 3, 5, 1, 5, 5, 7, 3, 5, 2, 6, 3, 6, 6, 9, 4, 8, 7, 7, 6, 7, 4, 6, 7, 8, 5, 6, 4, 7, 8, 9, 6, 6, 6, 9, 5, 7, 4, 8, 6, 10, 6, 5, 8, 11, 7, 10, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Conjecture: a(n) > 0 for all n > 3, and a(n) = 1 only for n = 4, 10, 12, 14, 16, 24, 36. This is analog of the conjecture in A237705 for squarefree numbers. We have verified the conjecture for n up to 60000. 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(10) = 1 since 7 and 3 are both prime, and there are exactly 3 squarefree numbers among 1, ..., 10-7. a(36) = 1 since 17 and 13 are both prime, and there are exactly 13 squarefree numbers among 1, ..., 36-17 (namely, 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19). MATHEMATICA s[n_]:=Sum[If[SquareFreeQ[k], 1, 0], {k, 1, n}] a[n_]:=Sum[If[PrimeQ[s[n-Prime[k]]], 1, 0], {k, 1, PrimePi[n-1]}] Table[a[n], {n, 1, 80}] CROSSREFS Cf. A000040, A005117, A013928, A237705, A237768, A237769, A238645. Sequence in context: A283472 A225538 A212355 * A194330 A280667 A194286 Adjacent sequences:  A238643 A238644 A238645 * A238647 A238648 A238649 KEYWORD nonn AUTHOR Zhi-Wei Sun, Mar 02 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.

Last modified December 4 12:24 EST 2021. Contains 349495 sequences. (Running on oeis4.)