A246374 Primes p such that if 2p-1 = product_{k >= 1} A000040(k)^(c_k), then p > product_{k >= 1} A000040(k-1)^(c_k).

5, 11, 13, 17, 23, 41, 43, 53, 59, 61, 73, 83, 113, 131, 137, 149, 163, 167, 173, 179, 193, 233, 239, 257, 263, 281, 293, 311, 313, 347, 353, 383, 389, 401, 419, 431, 443, 449, 463, 479, 491, 503, 509, 523, 557, 563, 587, 593, 599, 613, 617, 641, 653, 677, 683, 743, 761, 773, 787, 797

Offset: 1

Author

Antti Karttunen, Aug 25 2014

Keywords

• nonn

Comments

Primes p such that A064216(p) < p, or equally, A064989(2p-1) < p.

For all primes p here, 2p-1 must be composite (a necessary but not sufficient condition).

Examples

			5 is present, as 2*5 - 1 = 9 = p_2 * p_2, and p_1 * p_1 = 4, and 5 > 4.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A000040 and A246371.

A246373 gives the primes not here.

Cf. A000040, A064216, A064989.

Programs

PARI

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)};
n = 0; forprime(p=2,2^31, if((A064989((2*p)-1) < p), n++; write("b246374.txt", n, " ", p); if(n > 9999, break)));
(Scheme, with Antti Karttunen's IntSeq-library)
(define A246374 (MATCHING-POS 1 1 (lambda (n) (and (prime? n) (< (A064216 n) n)))))