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A052243 Initial prime in set of (at least) 4 consecutive primes in arithmetic progression with difference 30.

%I A052243 #78 Sep 08 2022 08:44:59
%S A052243 642427,1058861,3431903,4176587,4560121,4721047,5072269,5145403,
%T A052243 5669099,5893141,6248969,6285047,6503179,6682969,8545357,8776121,
%U A052243 8778739,9490571,9836227,9843019,9843049,10023787,11697979,12057919,12340313,12687119,12794641,12845849
%N A052243 Initial prime in set of (at least) 4 consecutive primes in arithmetic progression with difference 30.
%C A052243 Primes p such that p, p+30, p+60, p+90 are consecutive primes.
%C A052243 The analogous sequence for a CPAP-5 (at least five consecutive primes in arithmetic progression) with gap 30 does not have its own entry in the OEIS, but for over 500 terms it is identical to A059044. The CPAP-6 analog is A058362. - _M. F. Hasler_, Jan 02 2020
%H A052243 Chai Wah Wu, <a href="/A052243/b052243.txt">Table of n, a(n) for n = 1..10000</a> (terms n = 1..200 from M. F. Hasler)
%H A052243 OEIS wiki, <a href="/wiki/Consecutive_primes_in_arithmetic_progression#CPAP_with_given_gap">Consecutive primes in arithmetic progression: CPAP with given gap</a>, updated Jan. 2020.
%H A052243 <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>
%F A052243 A052243 = { A052195(n) | A052195(n+1) = A052195(n) + 30 }. - _M. F. Hasler_, Jan 02 2020
%e A052243 642427, 642457, 642487, 642517 are consecutive primes, so 642427 is in the sequence.
%p A052243 p := 2 : q := 3 : r := 5 : s := 7 : for i from 1 do if q-p = 30 and r-q=30 and s-r=30 then printf("%d,\n",p) ; fi ; p := q ; q := r ; r := s ; s := nextprime(r) ; od: # _R. J. Mathar_, Apr 12 2008
%t A052243 p=2; q=3; r=5; s=7; A052243 = Reap[For[i=1, i<1000000, i++, If[ q-p == 30 && r-q == 30 && s-r == 30 , Print[p]; Sow[p]]; p=q; q=r; r=s; s=NextPrime[r]]][[2, 1]] (* _Jean-François Alcover_, Jun 28 2012, after _R. J. Mathar_ *)
%t A052243 Transpose[Select[Partition[Prime[Range[1100000]],4,1],Union[ Differences[#]] =={30}&]][[1]] (* _Harvey P. Dale_, Jun 17 2014 *)
%o A052243 (PARI) A052243(n,p=2,print_all=0,g=30,c,o)={forprime(q=p+1,,if(p+g!=p=q, next, q!=o+2*g, c=2, c++>3, print_all&& print1(o-g","); n--||break); o=q-g);o-g} \\ optional 2nd arg specifies starting point, allows to define:
%o A052243 next_A052243(p)=A052243(1,p+1) \\ replacing older code from 2008. - _M. F. Hasler_, Oct 26 2018
%o A052243 (Magma) f:=func<n|NextPrime(n)>; a:=[]; for p in PrimesInInterval(2,13000000) do if  (f(p)-p eq 30) and (f(f(p))-p eq 60) and (f(f(f(p)))-p eq 90) then Append(~a,p); end if; end for; a; // _Marius A. Burtea_, Jan 04 2020
%Y A052243 Analogous sequences (start of CPAP-4 with common difference in square brackets): A033451 [6], A033447 [12], A033448 [18], A052242 [24], A052243 [this: 30], A058252 [36], A058323 [42], A067388 [48], A259224 [54], A210683 [60].
%Y A052243 Subsequence of A052195 and of A054800 (start of CPAP-4 with any common difference).
%Y A052243 See also A059044 (start of CPAP-5), A058362 (CPAP-6).
%K A052243 nonn
%O A052243 1,1
%A A052243 _Labos Elemer_, Jan 31 2000
%E A052243 More terms from _Harvey P. Dale_, Nov 19 2000
%E A052243 Edited by _N. J. A. Sloane_, Apr 28 2008, at the suggestion of _R. J. Mathar_