A129782 The upper twin prime whose lower member has a prime index.

5, 7, 13, 19, 43, 61, 181, 193, 433, 463, 601, 619, 1033, 1789, 2029, 2083, 2383, 2551, 3301, 4093, 4219, 4423, 4519, 4789, 5023, 5443, 5653, 9001, 9043, 9463, 10459, 13219, 13711, 13759, 14593, 14869, 15643, 16063, 16453, 16903, 17191, 17293

Offset

1,1

Comments

Computing and storing the indices of lower or upper twin primes is useful in computing twinl(n) or the n-th lower twin prime from a large file of primes.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

Every prime has an index denoting the position the prime is in the sequence 1,2,3,... For example, 5 is the 3rd prime number so 5 has index 3, 3 has index 2 etc. It is when an upper twin prime's lower member has an index that is also prime that we list the upper prime.

Example

13 is the upper twin prime of the pair 11,13. The lower member 11 is the 5th prime number and the index 5 is prime so 13 is in the table.

Mathematica

Select[Table[Prime[p], {p, Prime[Range[300]]}]+2, PrimeQ] (* Harvey P. Dale, Mar 07 2025 *)

Prog

(PARI) g(n) = for(x=1, n, p1=prime(x); p2=prime(x+1); if(p1+2==p2&&isprime(x), print1 (p2", ")))

Crossrefs

Sequence in context: A288632 A189557 A045444 * A080829 A224789 A078884

Adjacent sequences: A129779 A129780 A129781 * A129783 A129784 A129785

Keyword

easy,nonn,changed

Author

Cino Hilliard, May 17 2007

Status

approved