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%I #18 Sep 08 2022 08:46:11
%S 1,25,370,4015,4855,10945,36040,41425,41710,50455,56335,61900,81535,
%T 86995,116290,129700,134110,158365,207430,239635,255625,265990,267175,
%U 272815,293395,311590,335080,337810,339700,342115,365350,393385,403960,481345,488590,550990
%N Numbers n such that 4n+1, 4n+3, 4n+7, 4n+9 and 4n+13 are prime.
%C All terms in this sequence are 1 mod 3.
%C Each term yields a set of five consecutive primes.
%C Alternatively: Numbers n such that 4n+k forms a set of five consecutive primes for k = {1,3,7,9,13}.
%C Subsequence of A123986.
%H K. D. Bajpai, <a href="/A254376/b254376.txt">Table of n, a(n) for n = 1..8458</a>
%e 25 is in the list because 4*25 + 1 = 101, 4*25 + 3 = 103, 4*25 + 7 = 107, 4*25 + 9 = 109 and 4*25 + 13 = 113 are all prime.
%t Select[Range[1, 500000], PrimeQ[4*# + 1] && PrimeQ[4*# + 3] && PrimeQ[4*# + 7] && PrimeQ[4*# + 9] && PrimeQ[4*# + 13] &]
%t Select[Range[5*10^6], And @@ PrimeQ /@ ({1, 3, 7, 9, 13} + 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), print1(n,", ")))
%o (Magma) [n: n in [0..10^6] | forall{4*n+r: r in [1,3,7,9,13] | IsPrime(4*n+r)}]; // _Vincenzo Librandi_, Feb 16 2015
%Y Cf. A000040, A005098, A095278, A123986.
%K nonn
%O 1,2
%A _K. D. Bajpai_, Jan 29 2015
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