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%I #11 Aug 26 2014 01:29:22
%S 5,11,13,17,23,41,43,53,59,61,73,83,113,131,137,149,163,167,173,179,
%T 193,233,239,257,263,281,293,311,313,347,353,383,389,401,419,431,443,
%U 449,463,479,491,503,509,523,557,563,587,593,599,613,617,641,653,677,683,743,761,773,787,797
%N Primes p such that if 2p-1 = product_{k >= 1} A000040(k)^(c_k), then p > product_{k >= 1} A000040(k-1)^(c_k).
%C Primes p such that A064216(p) < p, or equally, A064989(2p-1) < p.
%C For all primes p here, 2p-1 must be composite (a necessary but not sufficient condition).
%H Antti Karttunen, <a href="/A246374/b246374.txt">Table of n, a(n) for n = 1..10000</a>
%e 5 is present, as 2*5 - 1 = 9 = p_2 * p_2, and p_1 * p_1 = 4, and 5 > 4.
%o (PARI)
%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o n = 0; forprime(p=2,2^31, if((A064989((2*p)-1) < p), n++; write("b246374.txt", n, " ", p); if(n > 9999, break)));
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (define A246374 (MATCHING-POS 1 1 (lambda (n) (and (prime? n) (< (A064216 n) n)))))
%Y Intersection of A000040 and A246371.
%Y A246373 gives the primes not here.
%Y Cf. A000040, A064216, A064989.
%K nonn
%O 1,1
%A _Antti Karttunen_, Aug 25 2014
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