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A084199 Smallest prime q < prime(n) such that q+1 divides prime(n)+1, a(n) = 1 if no such q exists.

%I A084199 #9 Mar 28 2025 04:12:45
%S A084199 1,1,2,3,2,1,2,3,2,2,3,1,2,3,2,2,2,1,3,2,1,3,2,2,13,2,3,2,1,2,3,2,2,3,
%T A084199 2,3,1,3,2,2,2,13,2,1,2,3,3,3,2,1,2,2,1,2,2,2,2,3,1,2,3,2,3,2,1,2,3,1,
%U A084199 2,13,2,2,3,1,3,2,2,1,2,1,2,1,2,13,3,2,2,1,2,3,2,2,3,2,3,2,2,2,3,1,3,2,2
%N A084199 Smallest prime q < prime(n) such that q+1 divides prime(n)+1, a(n) = 1 if no such q exists.
%C A084199 Conjecture: A008578 is the range of values (or A000040 = range of values > 1).
%H A084199 Amiram Eldar, <a href="/A084199/b084199.txt">Table of n, a(n) for n = 1..10000</a>
%F A084199 a(n) = 1 iff A084196(n) = 0.
%t A084199 seq[lim_] := Module[{p = Prime[Range[lim]], q, s = {}}, Do[q = SelectFirst[p, Divisible[p[[i]] + 1, # + 1] &]; AppendTo[s, If[q < p[[i]], q, 1]], {i, 1, Length[p]}]; s]; seq[100] (* _Amiram Eldar_, Mar 28 2025 *)
%Y A084199 Cf. A000040, A008578, A084196.
%K A084199 nonn
%O A084199 1,3
%A A084199 _Reinhard Zumkeller_, May 18 2003