A286313 Union of A078561 and A078562.

19, 31, 43, 61, 73, 79, 127, 157, 163, 229, 271, 349, 373, 379, 433, 439, 499, 607, 643, 673, 733, 751, 937, 967, 1009, 1093, 1213, 1279, 1291, 1429, 1489, 1543, 1549, 1597, 1609, 1657, 1777, 1861, 1987, 2131, 2203, 2287, 2341, 2347, 2371, 2383, 2389

Offset: 1

Author

Zak Seidov, May 06 2017

Keywords

• nonn

Comments

Number of terms among first 10^k primes, k=1..8:

0, 1, 17, 105, 646, 4385, 31721, 240346, 1884832.

E.g., k=1, first 10 primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and only 19 is a term of the sequence. - Zak Seidov, May 08 2017

Primes p such that prime(p+2) = p + 10. - Harvey P. Dale, Jan 13 2022

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..2000
• R. J. Mathar, Table of Prime Gap Constellations

Crossrefs

Cf. A078561 and A078562.

Programs

Maple

select(p -> isprime(p) and isprime(p+10) and (isprime(p+4) xor isprime(p+6)), [seq(i,i=5..10000,2)]); # Robert Israel, May 08 2017

Mathematica

Select[Prime[Range[1000]], NextPrime[#, 2] == # + 10 &]
Select[Partition[Prime[Range[400]],3,1],#[[1]]+10==#[[3]]&][[All,1]] (* Harvey P. Dale, Jan 13 2022 *)