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A216292 Values of k such that there is exactly one prime between 10k and 10k + 9.

%I A216292 #32 Sep 23 2022 10:14:56
%S A216292 9,11,12,14,18,21,24,29,30,36,39,41,42,45,47,48,55,58,63,66,68,69,71,
%T A216292 72,74,77,78,79,80,81,83,86,87,90,92,93,95,96,98,100,102,104,105,108,
%U A216292 111,116,117,119,120,124,125,131,137,138,139,140,144,147,151,152
%N A216292 Values of k such that there is exactly one prime between 10k and 10k + 9.
%H A216292 V. Raman, <a href="/A216292/b216292.txt">Table of n, a(n) for n = 1..10000</a>
%F A216292 a(n) ~ 0.1 n log n. - _Charles R Greathouse IV_, Sep 07 2012
%F A216292 a(n) = floor(A078494(n) / 10). - _Charles R Greathouse IV_, Sep 07 2012
%e A216292 36 is in the sequence because between 360 and 369 there is exactly one prime: 367. [_Bruno Berselli_, Sep 04 2012]
%t A216292 t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[Length[ps] == 1, AppendTo[t, n]], {n, 0, 199}]; t (* _T. D. Noe_, Sep 03 2012 *)
%t A216292 Select[Range[200],PrimePi[10#+9]-PrimePi[10#]==1&] (* _Harvey P. Dale_, Feb 04 2015 *)
%o A216292 (Magma) [n: n in [1..200] | IsOne(#PrimesInInterval(10*n, 10*n+9))]; // _Bruno Berselli_, Sep 04 2012
%o A216292 (PARI) is(n)=isprime(10*n+1)+isprime(10*n+3)+isprime(10*n+7)+isprime(10*n+9)==1 \\ _Charles R Greathouse IV_, Sep 07 2012
%o A216292 (Python)
%o A216292 from itertools import count, islice
%o A216292 from sympy import isprime
%o A216292 def A216292_gen(startvalue=1): # generator of terms >= startvalue
%o A216292     return filter(lambda k: sum(int(isprime(10*k+i)) for i in (1,3,7,9)) == 1, count(max(1,startvalue)))
%o A216292 A216292_list = list(islice(A216292_gen(),30)) # _Chai Wah Wu_, Sep 23 2022
%Y A216292 Cf. A007811, A032352, A078494, A216293.
%K A216292 nonn
%O A216292 1,1
%A A216292 _V. Raman_, Sep 03 2012