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A379677 Numbers k for which 10k+1, 10k+3, 10k+7, 10k+9, 10k+31, 10k+33, 10k+37, and 10k+39 are primes.

%I A379677 #11 Dec 31 2024 15:40:37
%S A379677 100630,259495,391921,960055,1053106,10881631,13144570,15237073,
%T A379677 15713164,17902876,21195025,25535221,26758786,55745863,68512435,
%U A379677 72449137,82135765,87141136,103026208,110310436,128216002,138120127,142769863,143237995,144399400,159672133,194876008
%N A379677 Numbers k for which 10k+1, 10k+3, 10k+7, 10k+9, 10k+31, 10k+33, 10k+37, and 10k+39 are primes.
%C A379677 k is a term if k and k+3 are both in A007811.
%F A379677 From _Hugo Pfoertner_, Dec 29 2024: (Start)
%F A379677 a(n) = (A059925(n) - 1)/10.
%F A379677 a(n) == 19 (mod 21). (End)
%e A379677 a(1) = 100630 since 1006301, 1006303, 1006307, 1006309, 1006331, 1006333, 1006337, and 1006339 are all prime and there are no smaller minimally close prime decades.
%o A379677 (Python)
%o A379677 from itertools import count
%o A379677 from sympy import isprime
%o A379677 def generate_a() :
%o A379677   for k in count() :
%o A379677     for j in (1,3,7,9,31,33,37,39) :
%o A379677       if not isprime(10*k+j) : break
%o A379677     else:
%o A379677       yield k
%Y A379677 Cf. A007811, A059925.
%K A379677 nonn
%O A379677 1,1
%A A379677 _Mike Speciner_, Dec 29 2024
%E A379677 More terms from _Hugo Pfoertner_, Dec 29 2024