Template:Sequence of the Day for August 22

Intended for: August 22, 2011

Timetable

• First draft entered by Alonso del Arte on May 28, 2011 as a verbatim copy of a write-up from December 22, 2010 ✓
• Draft reviewed by Alonso del Arte on August 21, 2011 ✓
• Draft approved by Daniel Forgues on August 21, 2011 ✓

Yesterday's SOTD * Tomorrow's SOTD

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A105999: Vos Post’s semiprimeth recurrence.

{ 1, 4, 10, 26, 77, 235, 779, ... }

Just as with Wilson’s primeth recurrence (see A007097), we start with 1 (even though it’s neither prime nor semiprime) and for the following terms use the recurrence

a (n) = spa (n  − 1)

(the semiprime equivalent of Wilson’s

a (n) = pa (n  − 1)

). I wonder if in this sequence 4 is the only square of a prime? (Quickest way to check several terms is to look for

μ (a (n)) = 0

, provided of course one has several terms).