A286313 - OEIS

%I #16 Jan 13 2022 13:16:23

%S 19,31,43,61,73,79,127,157,163,229,271,349,373,379,433,439,499,607,

%T 643,673,733,751,937,967,1009,1093,1213,1279,1291,1429,1489,1543,1549,

%U 1597,1609,1657,1777,1861,1987,2131,2203,2287,2341,2347,2371,2383,2389

%N Union of A078561 and A078562.

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

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

%C 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

%C Primes p such that prime(p+2) = p + 10. - _Harvey P. Dale_, Jan 13 2022

%H Harvey P. Dale, <a href="/A286313/b286313.txt">Table of n, a(n) for n = 1..2000</a>

%H R. J. Mathar, <a href="/A022004/a022004_1.pdf">Table of Prime Gap Constellations</a>

%p 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

%t Select[Prime[Range[1000]], NextPrime[#, 2] == # + 10 &]

%t Select[Partition[Prime[Range[400]],3,1],#[[1]]+10==#[[3]]&][[All,1]] (* _Harvey P. Dale_, Jan 13 2022 *)

%Y Cf. A078561 and A078562.

%K nonn

%O 1,1

%A _Zak Seidov_, May 06 2017