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%I #24 Sep 08 2022 08:46:11
%S 1,370,41425,81535,255625,267175,311590,365350,1054570,1381750,
%T 2533600,2975125,3266080,3930205,4684210,4782385,4802860,5940850,
%U 6414610,7986565,8429245,8570470,8636305,8810080,9270715,9857980,10459525,13708225,13917490,15127720,15252460
%N Numbers k such that 4*k + {1, 3, 7, 9, 13, 19} are all prime.
%C All terms in this sequence are congruent to 1 mod 3.
%C Subsequence of A123986.
%H Robert G. Wilson v, <a href="/A254288/b254288.txt">Table of n, a(n) for n = 1..1000</a> (first 726 terms from K. D. Bajpai)
%e a(2) = 370;
%e 4*370 + 1 = 1481;
%e 4*370 + 3 = 1483;
%e 4*370 + 7 = 1487;
%e 4*370 + 9 = 1489;
%e 4*370 + 13 = 1493;
%e 4*370 + 19 = 1499;
%e All six are prime.
%t Select[Range[5*10^7], PrimeQ[4*# + 1] && PrimeQ[4*# + 3] && PrimeQ[4*# + 7] && PrimeQ[4*# + 9] && PrimeQ[4*# + 13] && PrimeQ[4*# + 19] &]
%t Select[Range[5*10^6], And @@ PrimeQ /@ ({1, 3, 7, 9, 13, 19} + 4 #) &]
%o (PARI) for(n=1,10^7, if( isprime(4*n + 1) && isprime(4*n + 3) &&isprime(4*n + 7) &&isprime(4*n + 9) &&isprime(4*n + 13) &&isprime(4*n + 19) , print1(n,", ")))
%o (Magma) [n: n in [0..10^8] | forall{4*n+i: i in [1, 3, 7, 9, 13, 19] | IsPrime(4*n+i)}]; // _Vincenzo Librandi_, Mar 12 2015
%Y Cf. A000040, A005098, A095278, A123986.
%K nonn
%O 1,2
%A _K. D. Bajpai_, Jan 27 2015
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