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A032352 Numbers k such that there is no prime between 10*k and 10*k+9.

%I A032352 #50 Jul 06 2024 13:39:33
%S A032352 20,32,51,53,62,84,89,107,113,114,126,133,134,135,141,146,150,164,167,
%T A032352 168,171,176,179,185,189,192,196,204,207,210,218,219,232,236,240,248,
%U A032352 249,251,256,258,282,294,298,305,309,314,315,317,323,324,326,328,342
%N A032352 Numbers k such that there is no prime between 10*k and 10*k+9.
%C A032352 Numbers k with property that appending any single decimal digit to k does not produce a prime.
%C A032352 A007920(n*10) > 10.
%H A032352 M. I. Wilczynski, <a href="/A032352/b032352.txt">Table of n, a(n) for n = 1..10000</a>
%F A032352 a(n) ~ n. - _Charles R Greathouse IV_, Mar 29 2013
%e A032352 m=32: 321=3*107, 323=17*19, 325=5*5*13, 327=3*109, 329=7*47, therefore 32 is a term.
%p A032352 a:=proc(n) if map(isprime,{seq(10*n+j,j=1..9)})={false} then n else fi end: seq(a(n),n=1..350); # _Emeric Deutsch_, Aug 01 2005
%t A032352 f[n_] := PrimePi[10n + 10] - PrimePi[10n]; Select[ Range[342], f[ # ] == 0 &] (* _Robert G. Wilson v_, Sep 24 2004 *)
%t A032352 Select[Range[342], NextPrime[10 # ] > 10 # + 9 &] (* _Maciej Ireneusz Wilczynski_, Jul 18 2010 *)
%t A032352 Flatten@Position[10*#+{1,3,7,9}&/@Range@4000,{_?CompositeQ ..}] (* _Hans Rudolf Widmer_, Jul 06 2024 *)
%o A032352 (Haskell)
%o A032352 a032352 n = a032352_list !! (n-1)
%o A032352 a032352_list = filter
%o A032352    (\x -> all (== 0) $ map (a010051 . (10*x +)) [1..9]) [1..]
%o A032352 -- _Reinhard Zumkeller_, Oct 22 2011
%o A032352 (Magma) [n: n in [1..350] | IsZero(#PrimesInInterval(10*n, 10*n+9))]; // _Bruno Berselli_, Sep 04 2012
%o A032352 (PARI) is(n)=!isprime(10*n+1) && !isprime(10*n+3) && !isprime(10*n+7) && !isprime(10*n+9) \\ _Charles R Greathouse IV_, Mar 29 2013
%o A032352 (Python)
%o A032352 from sympy import isprime
%o A032352 def aupto(limit):
%o A032352   alst = []
%o A032352   for d in range(2, limit+1):
%o A032352     td = [10*d + j for j in [1, 3, 7, 9]]
%o A032352     if not any(isprime(t) for t in td): alst.append(d)
%o A032352   return alst
%o A032352 print(aupto(342)) # _Michael S. Branicky_, May 30 2021
%Y A032352 Cf. A124665 (subsequence), A010051, A007811, A216292, A216293.
%K A032352 nonn,base,easy
%O A032352 1,1
%A A032352 _Jeff Burch_
%E A032352 More terms from _Miklos Kristof_, Aug 27 2002