

A111183


First occurrence of prime(x)Pi(x) such that (Prime(x+1)  Pi(x+1))  (Prime(x)  Pi(x)) = k, k = 1,2,3,..


0



2, 3, 5, 15, 47, 19, 339, 80, 168, 128, 185, 196, 103, 275, 1771, 1871, 1028, 498, 3004, 851, 3641, 1087, 11845, 1613, 5402, 2404, 3182, 2889, 5225, 4190, 5461, 10585, 16958, 1280, 22444, 9357, 56241, 30129, 24857, 19006, 34461, 15852, 224417, 15401
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OFFSET

1,1


COMMENTS

Conjecture: There will always be an x such that a(x+1)  a(x) = k for k=1,2.. However, x becomes large when k > 70.


LINKS



FORMULA

Prime(x) = the xth prime. Pi(x) = number of primes <= x.


PROG

(PARI) primexmpix2(n) = \ Get first occurrence { local(x, y, z, c=0); for(k=1, 70, for(x=1, n, y=prime(x)primepi(x); z=prime(x+1)primepi(x+1); if(zy == k, print1(y", "); c++;; break; ) ) ); print(); print(c) }


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



