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A156204 First primes of an arithmetic progression of six primes with common difference 30.

%I A156204 #36 Sep 08 2022 08:45:41
%S A156204 7,107,359,541,2221,6673,7457,10103,25643,26861,27337,35051,56149,
%T A156204 61553,65557,73523,84317,110819,115733,131581,135151,137447,179321,
%U A156204 228587,243553,252163,279421,281717,310711,320119,337367,345487,347167,357079
%N A156204 First primes of an arithmetic progression of six primes with common difference 30.
%C A156204 Subsequence of A155760. - _R. J. Mathar_, Feb 07 2009
%C A156204 After the first term, all terms are congruent to 9 (mod 14). Gaps of 14 occur at a(n) = 22037759, 400852853, ... - _Zak Seidov_, Aug 01 2013
%C A156204 Subsequence of A227281. - _Zak Seidov_, Aug 26 2014
%C A156204 Note that a(n)+6*30 is composite for all n: a(1)+180 is divisible by 11 and for n>1 a(n)+180 is divisible by 7. - _Zak Seidov_, Apr 11 2015
%H A156204 Michael B. Porter, <a href="/A156204/b156204.txt">Table of n, a(n) for n = 1..10000</a>
%p A156204 for n from 1 to 60000 do p := ithprime(n) ; if isprime(p+30) and isprime(p+60) and isprime(p+90) and isprime(p+120) and isprime(p+150) then printf("%d,",p) ; fi; od: # _R. J. Mathar_, Feb 07 2009
%t A156204 Select[Range[360000], PrimeQ[#] && PrimeQ[# + 30] && PrimeQ[# + 60] && PrimeQ[# + 90] && PrimeQ[# + 120] && PrimeQ[# + 150] &] (* _Vincenzo Librandi_, Apr 13 2015 *)
%o A156204 (PARI) is_A156204(n) = isprime(n) && isprime(n+30) && isprime(n+60) && isprime(n+90) && isprime(n+120) && isprime(n+150) \\ _Michael B. Porter_, Aug 01 2013
%o A156204 (Magma) [p: p in PrimesUpTo(360000)| IsPrime(p+30) and IsPrime(p+60) and IsPrime(p+90)and IsPrime(p+120)and IsPrime(p+150)]; // _Vincenzo Librandi_, Apr 13 2015
%Y A156204 Cf. A155760, A227281.
%K A156204 nonn
%O A156204 1,1
%A A156204 _Ki Punches_, Feb 05 2009
%E A156204 Corrected and extended by _R. J. Mathar_ and _Ray Chandler_, Feb 08 2009