

A129470


Primes p such that the largest prime factor of p+1 has ErdosSelfridge class+ < N1 if p is of class N+.


7



883, 1747, 2417, 2621, 3181, 3301, 3533, 3571, 3691, 3853, 4027, 4133, 4513, 4783, 4861, 4957, 5303, 5381, 5393, 5563, 5641, 5821, 6067, 6577, 6991, 7177, 7253, 7331, 8059, 8093, 8377, 8731, 8839, 8929, 8969, 9221, 9281, 9397, 9613, 9931
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OFFSET

1,1


COMMENTS

In practice the class+ of a prime p is most often given by 1 + the class of the largest prime factor of p+1; elements of this sequence are counterexamples to this "rule". Elements of this sequence are at least of class 3+, since primes of class 1+ and 2+ have all prime factors of p+1 of class 1+. Elements a(k) of this sequence are >= 1+2*A005113[N1]*nextprime(A005113[N1]), where N is the class of a(k).


LINKS

Table of n, a(n) for n=1..40.


EXAMPLE

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 1+.


PROG

(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])}; A129470(n=100, p=1, a=[])={ local(f); while( #a<n, until( f[ #f] > 3, f=factor(1+p=nextprime(p+1))[, 1]); forstep( i=#f, 2, 1, f[i]=class( f[i] ); if( f[i] > f[ #f], a=concat(a, p); /*print(#a, " ", p); */ break))); a}


CROSSREFS

Cf. A129471A129473, A129477A129478, A129469, A005113, A005105A005108, A081633A081639, A084071, A090468, A129474A129475.
Sequence in context: A207054 A096992 A260926 * A129471 A023312 A129469
Adjacent sequences: A129467 A129468 A129469 * A129471 A129472 A129473


KEYWORD

easy,nonn


AUTHOR

M. F. Hasler, Apr 16 2007


STATUS

approved



