A129478 - OEIS

%I #3 Mar 31 2012 13:48:24

%S 17227801,18207913,18592957,19433053,19608073,19678081,20028121,

%T 20518177,20658193,20833213,21043237,21218257,21533293,21743317,

%U 22128361,22303381,23668537,25068697,25418737,25453741

%N Primes p of Erdos-Selfridge class 7+ with largest prime factor of p+1 not of class 6+.

%C See A129470

%e a(1) = 17227801 = -1+2*2917*2953 = A129469[7] is a prime of class 7+ since 17227801+1 has prime factor 2917 = A081634[1] = A005113[6] of class 6+, but the largest prime factor of 17227801+1 is 2953 = A005107[175] of class 3+.

%o (PARI) class(n,s=1)={n=factor(n+s)[,1];if(n[ #n]<=3,1,for(i=2,#n,n[1]=max(class(n[i],s)+1,n[1]));n[1])}; a129478(n=100,p=1,a=[])={local(f,a6=A005113[6]);p=max(p,a6*nextprime(a6+1)*2-2); while( #a<n, until( #f>2 & f[ #f-1] >= a6 & 6 > class(f[ #f]), f=factor(1+p=nextprime(p+1))[,1]); forstep( i=#f-1,2,-1, if( 7 < f[1] = max( f[1],1+class( f[i] )), next(2))); if( f[1] == 7, a=concat(a,p); print(#a," ",p))); a}

%Y Subsequence of A129470; see also A129471-A129473, A129477, A129469, A005113, A005105-A005108, A081633-A081635.

%K nonn

%O 1,1

%A _M. F. Hasler_, Apr 17 2007