A129469 Least prime of Erdos-Selfridge class n+ in A129470.

883, 3181, 15913, 2146141, 17227801, 456185017, 4960846573, 568124640697, 2273325467773, 145351829612377, 9302101084613641, 595332797734595317, 5813792718345189961, 1139502378775815768313, 166245781044286357673761

Offset: 3

Author

M. F. Hasler, Apr 16 2007

Keywords

• nonn

Comments

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*A005113(n-1)*p for all n<18, with p prime for n>3. This holds probably for all n.

Examples

			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+.
		

Crossrefs

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

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])}; 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, print("Warning, crossed a prime of class >= ",i+1,"+, p=", t[2]); ); ); print(i+2," ",t[3]); t[3])}