login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A238597 Number of primes p < 2*n with 2*pi(p) + 1 and p*(2n-1) - 2 both prime, where pi(.) is given by A000720. 2
0, 1, 2, 1, 1, 2, 2, 4, 1, 1, 5, 3, 1, 3, 1, 2, 4, 3, 3, 2, 2, 3, 4, 3, 1, 5, 3, 1, 3, 2, 4, 5, 2, 2, 2, 3, 3, 6, 3, 3, 4, 2, 4, 5, 3, 4, 5, 3, 2, 6, 2, 3, 8, 1, 1, 5, 5, 3, 5, 4, 4, 6, 2, 3, 3, 4, 3, 7, 3, 1, 7, 4, 4, 5, 4, 3, 8, 4, 1, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Conjecture: (i) a(n) > 0 for all n > 1, and a(n) = 1 for no n > 195.

(ii) For any integer n > 1, there is a prime p < 2*n with 2*pi(p) + 1 (or 2*pi(p) - 1) and 2*n + p both prime.

Part (i) of this conjecture is an extension of the conjecture in A238580.

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(9) = 1 since 5, 2*pi(5) + 1 = 2*3 + 1 = 7 and 5*(2*9-1) - 2 = 5*17 - 2 = 83 are all prime.

a(28) = 1 since 3, 2*pi(3) + 1 = 2*2 + 1 = 5 and 3*(2*28-1) - 2 = 3*55 - 2 = 163 are all prime.

a(195) = 1 since 71, 2*pi(71) + 1 = 2*20 + 1 = 41 and 71*(2*195-1) - 2 = 27617 are all prime.

MATHEMATICA

p[n_, k_]:=p[n, k]=PrimeQ[k]&&PrimeQ[2*PrimePi[k]+1]&&PrimeQ[k*(2n-1)-2]

a[n_]:=a[n]=Sum[If[p[n, k], 1, 0], {k, 1, 2n-1}]

Table[a[n], {n, 1, 80}]

CROSSREFS

Cf. A000040, A000720, A237284, A238580.

Sequence in context: A116560 A103784 A153916 * A045870 A229037 A036863

Adjacent sequences:  A238594 A238595 A238596 * A238598 A238599 A238600

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Mar 01 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 25 08:12 EST 2018. Contains 299646 sequences. (Running on oeis4.)