A129477 Primes p of Erdos-Selfridge class 6+ with largest prime factor of p+1 not of class 5+.

2146141, 2182897, 2954773, 3199813, 3224317, 3285577, 3383593, 3505933, 3555121, 3567373, 3653137, 3775417, 3864037, 4250977, 4298533, 4328053, 4493773, 4504651, 4519981, 4572037, 4647277, 4692637, 4719061, 4726537

Offset: 1

Author

M. F. Hasler, Apr 17 2007

Keywords

• easy
• nonn

Comments

See A129470

Examples

			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+.
		

Crossrefs

Subsequence of A129470; see also A129471-A129473, A129478, A129469, A005113, A005105-A005108, A081633-A081634.

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])}; a129477(n=100,p=1,a=[])={local(f,a5=A005113[5]);p=max(p,a5*nextprime(a5+1)*2-1); while( #a2 & 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}