A093502 a(1) = 2; for n > 0, a(n+1) is the a(n)-th prime after a(n).

2, 5, 19, 103, 733, 6691, 76831, 1081429, 18242699, 361919671, 8309068723, 217809953467, 6445388418589, 213232943658197, 7821073506524401, 315743571062703689

Offset: 1

Author

Amarnath Murthy, Apr 17 2004

Keywords

• more
• nonn

Comments

With prepended a(0) = 1 this is the lexicographically earliest infinite sequence such that A056239(a(n)) = a(n-1) + A056239(a(n-1)). - Antti Karttunen, Nov 02 2024

Examples

			19 follows 5 as there are 5 primes > 5 and up to 19 inclusive, (7,11,13,17,19).
		

Crossrefs

Cf. A000040, A000720, A056239, A074271.

Programs

Mathematica

a[1] := 2; a[n_] := Prime[PrimePi[a[n - 1]] + a[n - 1]]; Table[a[n], {n, 1, 10}] (* Stefan Steinerberger, Apr 10 2006 *)
NestList[Prime[PrimePi[ # ] + # ] &, 2, 13] (* Zak Seidov, Mar 21 2009 *)

Python

from sympy import prime
p, q = 2, 1
A093502_list = [p]
for _ in range(15):
    r = p + q
    p, q = prime(r), r
    A093502_list.append(p) # Chai Wah Wu, Jun 17 2019

Formula

a(n) = prime(pi(a(n-1)) + a(n-1)). - Vladeta Jovovic, Jun 19 2004

a(1)=2, a(n) = next a(n-1)th prime after a(n-1). - Zak Seidov, Mar 21 2009

a(n+1) = A000040(a(n) + index of a(n) in A000040). - David James Sycamore, Aug 20 2017

a(n) = A000040(A074271(n)), A056239(a(n)) = A074271(n). - Antti Karttunen, Nov 02 2024

Extensions

a(10) from Vladeta Jovovic, Jun 19 2004

More terms from Stefan Steinerberger, Apr 10 2006

a(13) from Zak Seidov, Mar 21 2009

a(14)-a(15) from Donovan Johnson, Dec 08 2009

Better definition from Jon E. Schoenfield, Aug 22 2017

a(16) from Chai Wah Wu, Jun 17 2019