A103575 Write the natural numbers as an infinite sequence of digits; starting at the left, cut into the smallest pieces so that each piece is a prime.

12345678910111, 2, 13, 14151617, 181, 920212223242526272829303132333435363738394041424344454647484950515253, 5

Offset: 1

Author

Alexandre Wajnberg, Mar 23 2005

Keywords

• base
• nonn

Comments

This is a "lossless" base-10 sequential-smallest-prime percolation of a Champernowne-substrate. The "lossy" version is A162324. The substrate percolates into identical terms 4-115 for both lossless and lossy versions. Terms 117-153 and 155-218 of the lossless version correspond to terms 119-155 and 158-221, respectively, of the lossy version. No other correspondences are known because of the subsequent interjection of very large primes. (For the purposes of this analysis, large probable primes have been treated as actual primes.)

Examples

			1 is not prime, 12 is not prime, 123 is not prime, 1234 is not prime, 12345 is not prime, etc. 1234567891 is prime but has to be rejected because the next term would begin with "0". The first one which works (thus the smallest one) is 12345678910111, matching the first 14 digits of the counting numbers, ... which is thus a(1).
The next digit of the counting numbers is 2 which is the smallest prime continuing the counting digits.
		

Links

• Hans Havermann, Indexed list of terms 1-257 (includes large probable primes)
• Dario Alpern, On-line routine to factor and prove primality
• Prime Pages, primality test

Extensions

Edited by Hans Havermann, Dec 07 2009