A162567 Primes p such that pi(p) divides p-1 and/or p+1, where pi(p) is the number of primes <= p.

2, 3, 5, 7, 11, 13, 29, 37, 43, 349, 359, 1087, 1091, 3079, 8423, 64579, 64591, 64601, 64609, 64661, 64709, 481043, 481067, 1304707, 3523969, 3524249, 3524317, 3524387, 9558541, 9559799, 9560009, 9560039, 25874767, 70115921, 189962009

Offset: 1

Author

Leroy Quet, Jul 06 2009

Keywords

• nonn

Examples

			The 10th prime is 29. Since 10 divides 29+1 = 30, 29 is in the sequence.
The 12th prime is 37. Since 12 divides 37-1 = 36, 37 is in the sequence.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..199 (data obtained from A048891 and A052013; sorted by Amiram Eldar Sep 05 2024)

Crossrefs

Union of A048891 and A052013. - Michel Marcus, Mar 04 2019

Cf. A000040, A078931.

Programs

Maple

isA162567 := proc(p) RETURN ( (p-1) mod numtheory[pi](p) = 0 or (p+1) mod numtheory[pi](p) = 0 ) ; end: for n from 1 to 50000 do p := ithprime(n) ; if isA162567(p) then printf("%d,",p) ; fi; od: # R. J. Mathar, Jul 30 2009
with(numtheory): a := proc (n) if `mod`(ithprime(n)-1, pi(ithprime(n))) = 0 or `mod`(ithprime(n)+1, pi(ithprime(n))) = 0 then ithprime(n) else end if end proc: seq(a(n), n = 1 .. 250000); # Emeric Deutsch, Jul 31 2009

Mathematica

Select[Prime[Range[11000000]],Or@@Divisible[{#-1,#+1},PrimePi[#]]&] (* Harvey P. Dale, Sep 08 2012 *)

Formula

a(n) = A000040(A078931(n)). - Alois P. Heinz, Feb 20 2023

Extensions

a(10)-a(35) from Donovan Johnson, Jul 29 2009