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A216288 Prime-free decades such that the next decade is also prime-free.

%I A216288 #21 Sep 08 2022 08:46:03
%S A216288 113,133,134,167,218,248,314,323,347,374,418,430,476,484,512,524,536,
%T A216288 545,560,575,596,640,650,674,692,708,713,726,737,776,797,833,839,847,
%U A216288 848,890,907,935,944,956,998,1001,1004,1037,1040,1080,1081,1091,1133,1175
%N A216288 Prime-free decades such that the next decade is also prime-free.
%C A216288 Numbers n such that 10n+1, 10n+3, 10n+7, 10n+9, 10n+11, 10n+13, 10n+17, and 10n+19 are composite. - _Charles R Greathouse IV_, Sep 07 2012
%H A216288 Charles R Greathouse IV, <a href="/A216288/b216288.txt">Table of n, a(n) for n = 1..10000</a>
%F A216288 a(n) ~ n. - _Charles R Greathouse IV_, Sep 07 2012
%F A216288 a(n) = A219998(n) - 1. - _V. Raman_, Dec 08 2012
%t A216288 ps0 = {2, 3, 5, 7}; t = {}; Do[ps1 = Select[Range[10*n, 10*n + 9], PrimeQ]; If[Length[ps0] == Length[ps1] == 0, AppendTo[t, n-1]]; ps0 = ps1, {n, 2, 1000}]; t (* _T. D. Noe_, Sep 03 2012 *)
%o A216288 (PARI) is(n)=nextprime(10*n)-10*n>20 \\ _Charles R Greathouse IV_, Sep 07 2012
%o A216288 (PARI) is(n)=!(isprime(10*n+1) || isprime(10*n+3) || isprime(10*n+7) || isprime(10*n+9) || isprime(10*n+11) || isprime(10*n+13) || isprime(10*n+17) || isprime(10*n+19)) \\ _Charles R Greathouse IV_, Sep 07 2012
%o A216288 (Magma) /* After the Greathouse's comment: */ [n: n in [0..1200] | forall{10*n+i: i in [1,3,7,9,11,13,17,19] | not IsPrime(10*n+i)}]; // _Bruno Berselli_, Sep 14 2012
%o A216288 (PARI) for(i=2, 1200, if(isprime(10*i+1)==0&&isprime(10*i+3)==0&&isprime(10*i+7)==0&&isprime(10*i+9)==0&&isprime(10*i+11)==0&&isprime(10*i+13)==0&&isprime(10*i+17)==0&&isprime(10*i+19)==0, print1(i", "))) /* V. Raman, Dec 08 2012 */
%Y A216288 Cf. A190639, A032352.
%Y A216288 Cf. A219998 (upper decade).
%K A216288 nonn,base
%O A216288 1,1
%A A216288 _V. Raman_, Sep 03 2012