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,..

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

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

Table of n, a(n) for n=1..44.

Formula

Prime(x) = the x-th 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(z-y == k, print1(y", "); c++;; break; ) ) ); print(); print(c) }

Crossrefs

Sequence in context: A120755 A227633 A270011 * A330821 A248827 A273525

Adjacent sequences: A111180 A111181 A111182 * A111184 A111185 A111186

Keyword

easy,nonn

Author

Cino Hilliard, Oct 22 2005

Status

approved