|
%I #48 Oct 30 2018 20:14:17
%S 111497,258527,286777,318407,332767,341827,358447,439787,473887,
%T 480737,495377,634187,647417,658367,663857,703837,732497,816317,
%U 819787,827767,843067,862307,937777,970457,970537,1001267,1012147,1032727,1052707,1055827,1104307,1117877,1164817,1165837
%N Initial prime in set of 4 consecutive primes with common difference 12.
%C From _Zak Seidov_, Sep 30 2014: (Start)
%C All terms are == {7, 17} mod 30. There is no set of 5 consecutive primes in arithmetic progression with common difference 12 (because a(n)+48 is always divisible by 5).
%C Minimal first difference a(n+1)-a(n) = 40, and this occurs first at a(709) = 26930767, a(11357) = 655389367 and a(23339) = 1510368877; all a(n) are == 7 mod 30. (End)
%H Zak Seidov, <a href="/A033447/b033447.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>
%t A033447 = Reap[For[p = 2, p < 1100000, p = NextPrime[p], p2 = NextPrime[p]; If[p2 - p == 12, p3 = NextPrime[p2]; If[p3 - p2 == 12, p4 = NextPrime[p3]; If[p4 - p3 == 12, Sow[p]]]]]][[2, 1]] (* _Jean-François Alcover_, Jun 28 2012 *)
%t Transpose[Select[Partition[Prime[Range[160000]],4,1],Union[ Differences[#]] =={12}&]][[1]] (* _Harvey P. Dale_, Jun 17 2014 *)
%o (PARI) A033447(n, p=2, show_all=1, g=12,c,o)={forprime(q=p+1,, if(p+g!=p=q, next, q!=o+2*g, c=2, c++>3, show_all&& print1(o-g", "); n--||break); o=q-g); o-g} \\ Can be used as next(p)=A033447(1, p+1) to get the next term, e.g.:
%o p=0; A033447_vec=vector(30,i,p=A033447(1,p+1)) \\ _M. F. Hasler_, Oct 26 2018
%Y Analogous sequences (start of CPAP-4 with common difference in square brackets): A033451 [6], this sequence [12], A033448 [18], A052242 [24], A052243 [30], A058252 [36], A058323 [42], A067388 [48], A259224 [54], A210683 [60].
%Y Subsequence of A052188 and of A248085. - _Zak Seidov_, Jun 27 2015
%Y Also subsequence of A054800: start of a CPAP-4, any common difference.
%K nonn
%O 1,1
%A _Jeff Burch_
%E More terms from _Labos Elemer_, Jan 31 2000
%E Definition clarified by _Harvey P. Dale_, Jun 17 2014
|
