Template:Sequence of the Day for August 20

Intended for: August 20, 2011

Timetable

• First draft entered by Alonso del Arte on May 29, 2011 as a verbatim copy of the write-up from December 19, 2010 ✓
• Draft reviewed by Alonso del Arte on August 12, 2011 ✓
• Draft approved by Daniel Forgues on August 13, 2011 ✓

Yesterday's SOTD * Tomorrow's SOTD

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A053169:

n

is in this sequence if and only if

n

is not in sequence A 

n

in the OEIS database.

{ 4, 7, 9, 11, 12, 13, 15, ... }

The number 40 is definitely not a prime number, yet in the OEIS it is the A-number that indexes the prime numbers (see A000040). Since early on, contributors to the OEIS have been interested in this kind of question. Since A-numbers are generally assigned by computer, and the computer has no directive to try to choose an A-number that would be “appropriate” or “ironic” for a given sequence, it is almost a matter of luck whether a new sequence will get an A-number that is in the sequence itself.

Here’s two puzzles for the day:

1. Should the number 53169 be in A053169? (Welcome to Russel’s paradox!)
2. Should the number 0 be in A053169? (Daniel Forgues had suggested using A000000 for the empty sequence, and Neil Sloane was amenable to the idea, but since that sequence has no terms, the lookup programs would not be able to handle it.)

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* See On-Line Encyclopedia of Integer Sequences#Self-referential sequences—Wikipedia.org.