A162324 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. Leading zeros are thrown away.

1234567891, 11, 1213, 14151617, 181, 920212223242526272829303132333435363738394041424344454647484950515253, 5

Offset

1,1

Comments

This is a "lossy" base-ten sequential-smallest-prime percolation of a Champernowne-substrate. The "lossless" version is A103575. The substrate percolates into identical terms 4-115 for both lossy and lossless versions. Terms 119-155 and 158-221 of the lossy version correspond to terms 117-153 and 155-218, respectively, of the lossless 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.)

Links

Table of n, a(n) for n=1..7.

Hans Havermann, Indexed list of terms 1-741 (includes large probable primes)

Example

After 1234567891 the next digit is 0 that has to be rejected. Next digits are 11 (prime); then 12, 13 (1213 prime); etc.

Crossrefs

A073175, A103575, A135605

Sequence in context: A167461 A135605 A091416 * A235640 A104953 A225139

Adjacent sequences: A162321 A162322 A162323 * A162325 A162326 A162327

Keyword

nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 01 2009

Extensions

Edited by Hans Havermann, Dec 07 2009

Status

approved