A128246 Number of twin prime members occurring in the sequence of prime-indexed primes for indices up to 10^n.

8, 37, 250, 2033, 17119, 144795, 1266584, 11272092, 101700063

Offset

1,1

Comments

Here prime(n) is the n-th prime number, pip(n) = prime(prime(n)) is the n-th prime-indexed prime.

The ratio of successive terms appears to converge. They are as follows for n = 2 to 6:

n pip(10^n) / pip(10^(n-1))

-- -----------------------------

2 4.625000000000000000000000000

3 6.756756756756756756756756757

4 8.132000000000000000000000000

5 8.420560747663551401869158878

6 8.458145919738302470938723056

Links

Table of n, a(n) for n=1..9.

Example

The first 10^1 prime-indexed primes are 3, 5, 11, 17, 31, 41, 59, 67, 83, 109. The 8 primes 3, 5, 11, 17, 31, 41, 59, 109 are also twin prime members. So 8 is the first term of this sequence.

Prog

(PARI) g(n) = c=0; for(x=1, n, y=prime(prime(x)); if(isprime(y+2)||isprime(y-2), c++)); c
(PARI) lista(pmax) = {my(ctwin = 0, cpip = 0, pow = 10, prev = 3, k = 2, isprev = 1, is); forprime(p = 5, , k++; is = isprime(k); if(isprev, cpip++); if(p == prev + 2 && (isprev || is), ctwin++); if(cpip == pow, print1(ctwin, ", "); pow* = 10); prev = p; isprev = is); } \\ Amiram Eldar, Jul 02 2024

Crossrefs

Cf. A001097, A006450.

Sequence in context: A221063 A221633 A201452 * A257215 A204076 A319960

Adjacent sequences: A128243 A128244 A128245 * A128247 A128248 A128249

Keyword

nonn,more

Author

Cino Hilliard, May 09 2007

Extensions

a(7)-a(9) from Amiram Eldar, Jul 02 2024

Status

approved