cp's OEIS Frontend

A270600 a(n) is the smallest k > 1 not already in the sequence such that p = prime(n) is a factor of 2^k-1.

%I A270600 #11 Mar 25 2016 07:49:40
%S A270600 2,4,3,10,12,8,18,11,28,5,36,20,14,23,52,58,60,66,35,9,39,82,22,48,
%T A270600 100,51,106,72,56,7,130,68,138,148,15,104,162,83,172,178,180,95,96,
%U A270600 196,99,210,37,226,76,29
%N A270600 a(n) is the smallest k > 1 not already in the sequence such that p = prime(n) is a factor of 2^k-1.
%C A270600 First differs from A014664 at n = 24.
%C A270600 a(n) is the smallest r such that p = prime(n) appears in row r of A060443 and r has not been the smallest such r for any previous p.
%C A270600 6 is not a term of the sequence, since 2^6-1 = 3^2 * 7, but 3 and 7 are already factors of 2^4-1 and 2^3-1 respectively.
%C A270600 Apart from 6, are there any other k > 1 that are not terms of the sequence?
%H A270600 Felix Fröhlich, <a href="/A270600/b270600.txt">Table of n, a(n) for n = 2..10000</a>
%o A270600 (PARI) nextk(p, k) = my(kk=k+1); while(Mod(2, p)^kk!=1, kk++); kk
%o A270600 isinvec(v, k) = for(x=1, #v, if(v[x]==k, return(1))); return(0)
%o A270600 addtovec(v, k) = my(w=vector(1)); w[1]=k; v=concat(v, w); v
%o A270600 addnextknotinvec(v, p) = my(kk=2); while(isinvec(v, kk), kk=nextk(p, kk)); addtovec(v, kk)
%o A270600 my(i=0, v=[], p=3); while(i < 50, v=addnextknotinvec(v, p); p=nextprime(p+1); i++); v
%Y A270600 Cf. A014664, A060443.
%K A270600 nonn
%O A270600 2,1
%A A270600 _Felix Fröhlich_, Mar 20 2016