The On-Line Encyclopedia of Integer Sequences (OEIS)

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First occurrence of prime(x)-Pi(x) such that (Prime(x+1) - Pi(x+1)) - (Prime(x) - Pi(x)) = k, k = 1,2,3,..
(history; published version)

#3 by N. J. A. Sloane at Tue Oct 01 17:58:20 EDT 2013

AUTHOR

_Cino Hilliard (hillcino368(AT)gmail.com), _, Oct 22 2005

Discussion

Tue Oct 01

17:58

OEIS Server: https://oeis.org/edit/global/1955

#2 by N. J. A. Sloane at Wed Dec 06 03:00:00 EST 2006

KEYWORD

easy,nonn,new

AUTHOR

Cino Hilliard (hillcino368(AT)hotmailgmail.com), Oct 22 2005

#1 by N. J. A. Sloane at Tue Jan 24 03:00:00 EST 2006

NAME

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

DATA

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.

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) }

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard (hillcino368(AT)hotmail.com), Oct 22 2005

STATUS

approved