A110896 Difference between prime(10^n) and prime(10^(n-1)).

27, 512, 7378, 96810, 1194980, 14186154, 163938810, 1858650070, 20763688746, 229296037134, 2508629501894, 27235496973316, 293784284670498, 3151605249578196, 33649122286540910, 357782405858669892, 3790389667563960340, 40026493653364473662, 421463674881774896218

Offset: 1

Author

Cino Hilliard, Sep 20 2005

Keywords

• nonn

Examples

			The (10^1)th prime is 29. The (10^0)th prime is 2 and the difference is 27 the first entry.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..24

Crossrefs

Cf. A000040, A006988, A135371, A135373.

Programs

Mathematica

Table[Prime[10^n] - Prime[10^(n - 1)], {n, 1, 12}] (* Marvin Ray Burns, Dec 09 2007 *)
Differences[Table[Prime[10^n],{n,0,12}]] (* Harvey P. Dale, Jul 03 2017 *)

PARI

a(n) = prime(10^n) - prime(10^(n-1)); \\ Jinyuan Wang, Nov 14 2020; adapted to offset by Georg Fischer, Jun 22 2022

Python

from sympy import prime
def a(n): return prime(10**n)-prime(10**(n-1))
print([a(n) for n in range(1, 10)]) # Michael S. Branicky, Jun 22 2022

Formula

a(n) = A006988(n) - A006988(n-1) = prime(10^n) - prime(10^(n-1)). - Marvin Ray Burns, Dec 09 2007; corrected by Michel Marcus, Jun 22 2022

Extensions

Corrected and extended by Marvin Ray Burns, Dec 09 2007

More terms from Jinyuan Wang, Nov 14 2020