A033186 Remove all 2's from decimal expansion of Pi, then all 3's, ..., then all 11's, ... (running through primes in order) with the restriction that only digits contiguous in the original expansion are removed.

1, 9, 6, 9, 8, 4, 6, 6, 4, 8, 9, 0, 8, 8, 4, 1, 6, 9, 9, 9, 1, 0, 8, 0, 9, 4, 9, 4, 4, 9, 0, 8, 1, 6, 4, 0, 6, 8, 6, 0, 9, 8, 6, 8, 0, 4, 8, 4, 0, 6, 9, 8, 1, 4, 8, 0, 8, 6, 1, 8, 0, 6, 6, 4, 0, 9, 0, 8, 1, 9, 4, 0, 8, 1, 8, 4, 8, 1, 4, 0, 8, 0, 0, 8, 0, 9, 6

Offset

1,2

Comments

The condition to remove only contiguous digits in the original expansion ensures this sequence is well-defined. If the sequence were to be "closed up" after each prime removed, then any given initial portion will (almost certainly) be the prefix of some prime larger than those removed so far. - Sean A. Irvine, Jul 06 2020

The sequence of primes removed is given by A033274. - Sean A. Irvine, Jul 05 2020

Links

Sean A. Irvine, Table of n, a(n) for n = 1..8200

Sean A. Irvine, Java program (github)

Example

From Sean A. Irvine, Jul 05 2020: (Start)
Using "z" to denote deleted portions:
  31415926535897932...
  314159z653589793z...  (replace 2)
  z14159z65z58979zz...  (replace 3)
  z141z9z6zzz8979zz...  (replace 5)
  z141z9z6zzz89z9zz...  (replace 7)
  ...
  z1zz9z6zzz89z9zz...   (replace 41)
  ...
  z1zz9z6zzzzz9zz...    (replace 89)
Hence sequence starts, 1, 9, 6, 9, ...
(End)

Crossrefs

Sequence in context: A230161 A345288 A019790 * A146486 A137907 A070164

Adjacent sequences: A033183 A033184 A033185 * A033187 A033188 A033189

Keyword

nonn,base

Author

Simon Plouffe

Extensions

Definition and data modified by Simon Plouffe and Sean A. Irvine, Jul 05 2020

Status

approved