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%I A129474 #10 Dec 14 2017 19:53:51
%S A129474 1704961513,7281416041,7638227617,9462536833,11934730597,13237911481,
%T A129474 13282423003,13522629793,13942983841,14185279861,16029089501,
%U A129474 16221987853,17434233041,18171787987,19639505461,20717555041
%N A129474 Primes of Erdos-Selfridge class 14+.
%C A129474 Primes of class r (or r+) are by definition the primes p for which p + 1 has all factors of a lower class < r, but at least one factor of class r - 1. See A005113 for more information.
%C A129474 a(1..149) calculated using A090468 up to 37.5e9, which gives A129474(150) > 75e9.
%H A129474 M. F. Hasler, <a href="/A129474/b129474.txt">Table of n, a(n) for n = 1..149</a>
%F A129474 { a(n) } = { p = 2*m*A090468(k)-1 | k=1,2,3... and m=1,2,3... such that p is prime and m has no factor of class > 13+ }
%e A129474 a(1) = A005113[14] = 1704961513 = -1+2*852480757, where 852480757 = A090468[2]
%o A129474 (PARI) class(n, s=1) = { if(!isprime(n),0, if(!(n=factor(n+s)[,1]) || n[ #n]<=3,1, for(i=2,#n,n[1]=max(class(n[i],s)+1,n[1]));n[1]))};
%o A129474 nextclass(a,s=1,p,n=[])={if(!p,p=nextprime(a[ #a]+1)); print("producing primes of class ",1+class(a[1],s),["+","-"][1+(s<0)]," up to 2*",p); for(i=1,#a,for(k=1,p/a[i],if(isprime(2*k*a[i]-s),n=concat(n,2*k*a[i]-s))));vecsort(n)};
%o A129474 A129474=nextclass(A090468,1)
%Y A129474 Cf. A005113, A005105-A005108, A081633-A081639, A084071, A090468, A129475.
%K A129474 nonn
%O A129474 1,1
%A A129474 _M. F. Hasler_, Apr 16 2007

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