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%I #3 Mar 31 2012 13:48:24
%S 2146141,2182897,2954773,3199813,3224317,3285577,3383593,3505933,
%T 3555121,3567373,3653137,3775417,3864037,4250977,4298533,4328053,
%U 4493773,4504651,4519981,4572037,4647277,4692637,4719061,4726537
%N Primes p of Erdos-Selfridge class 6+ with largest prime factor of p+1 not of class 5+.
%C See A129470
%e a(1) = 2146141 = -1+2*1021*1051 = A129469[6] is a prime of class 6+ since 2146141+1 has prime factor 1021=A081633[1]=A005113[5] of class 5+, but the largest prime factor of 2146141+1 is 1051=A005107[65] 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])}; a129477(n=100,p=1,a=[])={local(f,a5=A005113[5]);p=max(p,a5*nextprime(a5+1)*2-1); while( #a<n, until( #f>2 & f[ #f-1] >= a5 & 5 > class(f[ #f]), f=factor(1+p=nextprime(p+1))[,1]); forstep( i=#f-1,2,-1, if( 6 < f[1] = max( f[1],1+class( f[i] )), next(2))); if( f[1] == 6, a=concat(a,p); print(#a," ",p))); a}
%Y Subsequence of A129470; see also A129471-A129473, A129478, A129469, A005113, A005105-A005108, A081633-A081634.
%K easy,nonn
%O 1,1
%A _M. F. Hasler_, Apr 17 2007