A129478 Primes p of Erdos-Selfridge class 7+ with largest prime factor of p+1 not of class 6+.

17227801, 18207913, 18592957, 19433053, 19608073, 19678081, 20028121, 20518177, 20658193, 20833213, 21043237, 21218257, 21533293, 21743317, 22128361, 22303381, 23668537, 25068697, 25418737, 25453741

Offset: 1

Author

M. F. Hasler, Apr 17 2007

Keywords

• nonn

Comments

See A129470

Examples

			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+.
		

Crossrefs

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

Programs

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( #a2 & 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}