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A129474 Primes of Erdos-Selfridge class 14+. 8

%I

%S 1704961513,7281416041,7638227617,9462536833,11934730597,13237911481,

%T 13282423003,13522629793,13942983841,14185279861,16029089501,

%U 16221987853,17434233041,18171787987,19639505461,20717555041

%N Primes of Erdos-Selfridge class 14+.

%C 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 a(1..149) calculated using A090468 up to 37.5e9, which gives A129474(150) > 75e9.

%H M. F. Hasler, <a href="/A129474/b129474.txt">Table of n, a(n) for n = 1..149</a>

%F { 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 a(1) = A005113[14] = 1704961513 = -1+2*852480757, where 852480757 = A090468[2]

%o (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 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=nextclass(A090468,1)

%Y Cf. A005113, A005105-A005108, A081633-A081639, A084071, A090468, A129475.

%K nonn

%O 1,1

%A _M. F. Hasler_, Apr 16 2007

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Last modified May 22 00:25 EDT 2019. Contains 323472 sequences. (Running on oeis4.)