A059925 - OEIS

%I #37 Dec 29 2024 20:24:19

%S 1006301,2594951,3919211,9600551,10531061,108816311,131445701,

%T 152370731,157131641,179028761,211950251,255352211,267587861,

%U 557458631,685124351,724491371,821357651,871411361,1030262081,1103104361,1282160021,1381201271,1427698631,1432379951,1443994001

%N Numbers n such that {n, n+2, n+6, n+8, n+30, n+32, n+36, n+38} are all prime.

%C Each term is the initial member of two prime quadruples (A007530) with the smallest possible difference of 30.

%H Jud McCranie and Sebastian Petzelberger, <a href="/A059925/b059925.txt">Table of n, a(n) for n = 1..10000</a> (first 1238 terms from Jud McCranie)

%H J. Brüggemann, <a href="http://ymmij.de/Nerd/p4/p4-2.pdf">The twins of prime quadruples up to 10^17</a> [71 MB].

%H D. La Pierre Ballard, <a href="http://www.teapro.com/fixpnq30.html">Prime Number Quadruplets 30 Apart</a>

%F a(n) = 2 (mod 21). - _Hugo Pfoertner_, Dec 29 2024

%t Select[Prime[Range[5582*10^4]],AllTrue[#+{2,6,8,30,32,36,38},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Mar 13 2019 *)

%o (PARI) is(n)=my(v=[0,2,6,8,30,32,36,38]);for(i=1,8, if(!isprime(n+v[i]), return(0)));1 \\ _Charles R Greathouse IV_, Jun 18 2013

%Y Cf. A007530, A256842.

%K nonn

%O 1,1

%A _Martin Raab_, Mar 03 2001

%E For clarity, replaced definition by a comment from _Charles R Greathouse IV_. - _N. J. A. Sloane_, Nov 26 2020