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

Author

Simon Plouffe

Keywords

• nonn
• base

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

Examples

			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)
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..8200
• Sean A. Irvine, Java program (github)

Extensions

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