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A089091 a(n) is the smallest composite number coprime to n and n+1.

%I A089091 #18 Aug 16 2023 01:34:47
%S A089091 9,25,25,9,49,25,9,25,49,9,25,25,9,121,49,9,25,25,9,121,25,9,25,49,9,
%T A089091 25,25,9,49,49,9,25,25,9,121,25,9,25,49,9,25,25,9,49,49,9,25,25,9,49,
%U A089091 25,9,25,49,9,25,25,9,49,49,9,25,25,9,49,25,9,25,121,9,25,25,9,49,49,9,25,25
%N A089091 a(n) is the smallest composite number coprime to n and n+1.
%F A089091 a(n) = A053670(n)^2.
%t A089091 m=0;Table[fla=1;Do[s=GCD[n, k]; s1=GCD[n, k+1];s2=GCD[n, k+2];s3=GCD[n, k+3]; If[Equal[s, 1]&&Equal[s1, 1]&&!PrimeQ[n]&&!Equal[n, 1]&& Equal[fla, 1], m=m+1;Print[n];fla=0], {n, 1, 1000}], {k, 1, 256}]
%o A089091 (Python)
%o A089091 from math import gcd
%o A089091 def a(n):
%o A089091     k, m = 3, n*(n+1)
%o A089091     while gcd(k, m) != 1: k += 2
%o A089091     return k*k
%o A089091 print([a(n) for n in range(1, 79)]) # _Michael S. Branicky_, Sep 25 2021
%Y A089091 Cf. A007978, A053669, A053670, A053671, A053672, A053673, A053674.
%Y A089091 Cf. A090092, A090093.
%K A089091 easy,nonn
%O A089091 1,1
%A A089091 _Labos Elemer_, Nov 26 2003
%E A089091 Offset corrected by _Mohammed Yaseen_, Aug 15 2023