3,1

The sequence starts at offset 3, since primes of class 1+ and 2+ have all prime factors (of p+1) of class 1+. Definitions imply that a(n) >= -1+2*A005113(n-1)*nextprime(1+A005113(n-1)). We have a(n) = -1+2*A5113(n-1)*p for all n<18, with p prime for n>3. This holds probably for all n.

a(3) = 883 = -1+2*13*17 is a prime of class 3+ since 13 is of class 2+, but the largest divisor of 883+1 is 17 which is only of class 2+.

a(4) = 3181 = -1+2*37*43 is a prime of class 4+ since 37 is of class 3+, but the largest divisor of 3181+1 is 43 which is only of class 2+.

(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])}; A129469={vector(#A005113-1, i, t=A005113[i+1]; t=[t, nextprime(t+1)-1, 0]; until( isprime( t[3] = -1+2*t[1]*t[2] ) & (f=factor( 1+t[3] )[, 1]) & class(f[ #f], 1)<i+1, while( isprime( t[2]++ ) && class( t[2], 1) >= i+1, print("Warning, crossed a prime of class >= ", i+1, "+, p=", t[2]); ); ); print(i+2, " ", t[3]); t[3])}

Cf. A129470, A005113, A005105 - A005108, A081633 - A081639, A084071, A090468, A129474 - A129475.

Sequence in context: A129470 A129471 A023312 this_sequence A031794 A020393 A103811

Adjacent sequences: A129466 A129467 A129468 this_sequence A129470 A129471 A129472

nonn

M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Apr 16 2007