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A113496 a(n) = smallest composite integer > c(n) and coprime to c(n), where c(n) is the n-th composite integer.

%I A113496 #17 Mar 28 2021 15:54:16
%S A113496 9,25,9,10,21,25,15,16,21,25,21,22,25,25,26,27,28,33,49,33,34,35,36,
%T A113496 49,39,40,49,55,45,46,49,49,50,51,52,55,55,56,57,58,63,77,63,64,65,66,
%U A113496 85,69,70,81,77,75,76,77,78,85,81,82,85,85,86,87,88,91,91,92,93,94,95,96
%N A113496 a(n) = smallest composite integer > c(n) and coprime to c(n), where c(n) is the n-th composite integer.
%F A113496 a(n) = A113484(A002808(n)). - _Robert G. Wilson v_, Jan 12 2006
%t A113496 Composite[n_Integer] := FixedPoint[n + PrimePi[ # ] + 1 &, n + PrimePi[n] + 1]; f[n_] := Block[{k = n + 1}, While[PrimeQ@k || GCD[k, n] > 1, k++ ]; k]; Array[ f[ Composite[ # ]] &, 70] (* _Robert G. Wilson v_, Jan 12 2006 *)
%o A113496 (Python)
%o A113496 from sympy import isprime, gcd, composite
%o A113496 def A113496(n):
%o A113496     m = composite(n)
%o A113496     k = m+1
%o A113496     while gcd(k,m) != 1 or isprime(k):
%o A113496         k += 1
%o A113496     return k # _Chai Wah Wu_, Mar 28 2021
%Y A113496 Cf. A002808, A113484.
%K A113496 nonn
%O A113496 1,1
%A A113496 _Leroy Quet_, Jan 11 2006
%E A113496 More terms from _Robert G. Wilson v_, Jan 12 2006