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A244435 a(n) is the smallest number m such that 2*k*m - 1 is composite for all k, 0 < k < n+1.

%I A244435 #16 Nov 10 2024 02:24:20
%S A244435 5,13,13,62,73,73,89,118,118,118,118,118,236,926,959,959,959,959,959,
%T A244435 959,1063,1474,1474,1474,1667,1667,6118,8249,9098,9098,9098,9098,9098,
%U A244435 9098,9098,9098,9098,9098,9098,9098,9098,9098,9098,35573,35573,35573,57448,57448,57448,57448,57448,57448,57448
%N A244435 a(n) is the smallest number m such that 2*k*m - 1 is composite for all k, 0 < k < n+1.
%C A244435 a(2)=a(3)=13, a(5)=a(6)=73, ... a(29)=a(30)=...=a(43)=9098, ... . A244436 gives numbers k such that a(k) is not in the set {a(k-1), a(k+1)}.
%H A244435 Robert Israel, <a href="/A244435/b244435.txt">Table of n, a(n) for n = 1..164</a>
%p A244435 M:= 0: R:= NULL:
%p A244435 for m from 2 while M < 100 do
%p A244435   for i from 0 while not isprime(2*i*m-1) do od:
%p A244435   if i-1 > M then R:= R, m$(i-1-M); M:= i-1; fi;
%p A244435 od:
%p A244435 R; # _Robert Israel_, May 03 2021
%o A244435 (PARI) isok(n, m) = for(k=1, n, my(x=2*k*m-1); if ((x==1) || isprime(x), return(0))); return (1);
%o A244435 a(n) = my(m=1); while(!isok(n, m), m++); m; \\ _Michel Marcus_, May 04 2021
%Y A244435 Cf. A124516, A244433, A244436.
%K A244435 nonn
%O A244435 1,1
%A A244435 _Farideh Firoozbakht_, Jul 19 2014