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Smallest prime(k) such that 2^n divides the product of composite numbers between prime(k) and prime(k+1) but 2^(n+1) does not.
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%I #9 Mar 05 2024 12:40:19

%S 2,5,3,19,7,13,23,47,31,89,139,113,199,293,631,317,1069,509,2503,1129,

%T 1759,2039,887,1951,4027,3967,2477,2971,3271,6917,4831,5591,10799,

%U 5119,14107,9973,1327,39461,16381,20809,11743,15683,61169,52391,33247,45439

%N Smallest prime(k) such that 2^n divides the product of composite numbers between prime(k) and prime(k+1) but 2^(n+1) does not.

%e a(0) = 2, a(1) = 5, a(2) = 3 a(5) = 13 as 2^5 = 32 divides 14*15*16 but 2^6=64 does not.

%t f[n_] := Block[{k = 1}, While[ Mod[Times @@ Select[ Range[Prime@k, Prime[k + 1]], ! PrimeQ@# &], 2^n] != 0 || Mod[Times @@ Select[ Range[Prime@k, Prime[k + 1]], ! PrimeQ@# &], 2^(n + 1)] == 0, k++ ]; Prime@k]; Table[ f[n], {n, 0, 45}] (* _Robert G. Wilson v_, Apr 06 2006 *)

%K nonn

%O 0,1

%A _Amarnath Murthy_, Nov 02 2002

%E More terms from _Robert G. Wilson v_, Apr 06 2006