A087382 Twin prime indices of primes forming a twin prime member.

3, 5, 7, 11, 13, 17, 29, 41, 43, 61, 109, 149, 179, 191, 269, 313, 347, 431, 461, 463, 601, 617, 643, 659, 829, 859, 1031, 1033, 1051, 1231, 1279, 1321, 1619, 1621, 1879, 1931, 1949, 1999, 2029, 2309, 2311, 2341, 2383, 2711, 2789, 2791, 2801, 3253, 3299, 3329

Offset

3,1

Comments

It is interesting that these primes occur rather frequently early on but gradually diminish as the iterations increase. Some ratios of count of twin primes p and the occurrence of prime(p) also a twin prime is as follows. Index< Ratio 1000 .74 10000 .48 100000 .39 1000000 .35 Looks like it is approaching a limit.

Links

Table of n, a(n) for n=3..52.

Example

The 29th prime,109,is also a twin prime paired with the prime 107.

Prog

(PARI) twips(n) = { c1=0; c2=0; forprime(x=3, n, if(isprime(x+2), c1++); x1=prime(x); if(isprime(x-2) || isprime(x+2), if(isprime(x1-2) || isprime(x1+2), print1(x", "); c2++; ) ) ); print(); print(c2/c1+.0) }

Crossrefs

Sequence in context: A088503 A118939 A239391 * A355845 A025127 A024883

Adjacent sequences: A087379 A087380 A087381 * A087383 A087384 A087385

Keyword

easy,nonn

Author

Cino Hilliard, Oct 21 2003

Status

approved