cp's OEIS Frontend

A158895 A list of primes written in order of their first appearance in a table of prime factorizations of 2^k+1, k=1,2,... .

%I A158895 #14 Jan 03 2018 23:20:13
%S A158895 3,5,17,11,13,43,257,19,41,683,241,2731,29,113,331,65537,43691,37,109,
%T A158895 174763,61681,5419,397,2113,2796203,97,673,251,4051,53,157,1613,87211,
%U A158895 15790321,59,3033169,61,1321,715827883
%N A158895 A list of primes written in order of their first appearance in a table of prime factorizations of 2^k+1, k=1,2,... .
%C A158895 This sequence has the property that if a(n) appears first in the table as a prime factor of 2^m+1 for some m then a(n)=2*k*m+1 for some k.
%C A158895 When, for some m, 2^m+1 has more than one prime factor appearing in the table for the first time, we adopt the convention of entering them in ascending order. For example, the entries ..., 29, 113, ... both arise from 2^14+1.
%H A158895 Harvey P. Dale and Charles R Greathouse IV, <a href="/A158895/b158895.txt">Table of n, a(n) for n = 1..4017</a> (first 650 terms from Dale)
%e A158895 2^1+1=3, 2^2+1=5, 2^3+1=3^2 and 2^4+1=17. Thus a(1)=3, a(2)=5 and a(3)=17, on noting that 2^3+1 contributes no new prime factors.
%t A158895 DeleteDuplicates[Flatten[Table[Transpose[FactorInteger[2^k+1]][[1]],{k,50}]]] (* _Harvey P. Dale_, Mar 30 2014 *)
%o A158895 (PARI) lista(n)=prs = Set(); for (k=1, n, f = factor(2^k+1); for (i=1, length(f~), onef = f[i,1]; if (! setsearch(prs, onef), print1(onef, ", "); prs = setunion(prs, Set(onef));););); \\ _Michel Marcus_, Apr 18 2013
%o A158895 (PARI) G=1; for(n=1,500, g=gcd(f=2^n+1,G); while(g>1, g=gcd(g,f/=g)); f=factor(f)[,1]; if(#f, for(i=1,#f, print1(f[i]", ")); G*=factorback(f))) \\ _Charles R Greathouse IV_, Jan 03 2018
%Y A158895 Subsequence of A001269.
%Y A158895 Cf. A002587, A066845, A108974.
%K A158895 nice,nonn
%O A158895 1,1
%A A158895 _Martin Griffiths_, Mar 29 2009