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A129470
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Primes p such that the largest prime factor of p+1 has Erdős-Selfridge class+ < N-1 if p is of class N+.
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7
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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
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1,1
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COMMENTS
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In practice the class+ of a prime p is most often given by 1 + the class of the largest prime factor of p+1; terms of this sequence are counterexamples to this "rule". Terms 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+. Terms a(k) of this sequence are >= -1 + 2*A005113(N-1) * nextprime(A005113(N-1)), where N is the class of a(k).
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LINKS
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EXAMPLE
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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+.
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PROG
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(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}
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CROSSREFS
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Cf. A005105, A005106, A005107, A005108, A005113, A081633, A081634, A081635, A081636, A081637, A081638, A081639, A084071, A090468, A129469, A129471, A129472, A129473, A129474, A129475, A129477, A129478.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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