A146563 First instance prime-cover Sierpinski bases.

14, 74, 339, 2601, 32400

Offset

2,1

Comments

A prime-cover Sierpinski base is the lowest base b such that k*b^n + 1 can generate a Sierpinski number from cover sets with prime length. For example, b = 14 provides Sierpinski number k = 4 such that 4*14^n + 1 is always composite for any integer n. The covering set comprises 2 primes each providing prime factors for even or odd values of n in k*b^n + 1, so-called 2-cover, 2 = 1st prime. Sequence generated for 2-, 3-, 5- 7- and 11-cover.

Links

Table of n, a(n) for n=2..6.

Exotic covers

Robert Gerbicz, Covering Sets

Formula

To generate a term of the sequence, we must find the smallest value of b such that b^p - 1 has at least p prime factors of the form 1 mod p, excluding any p in b - 1. The exclusion ensures that covers are not trivial, with all n being factored by a particular prime.

Example

The corresponding k values providing the lowest Sierpinski numbers generated by known minimal k Sierpinski numbers for prime-covers are 4*14^n + 1 (2-cover), 2012*74^n + 1 (3-cover), 84536206*339^n + 1 (5-cover), unknown*2601^n + 1 (7-cover), and unknown*32400^n + 1 (11-cover).

Prog

(C) // See the Robert Gerbicz link for bigcovering.c.

Crossrefs

Sequence in context: A369244 A213284 A232377 * A205583 A167633 A196411

Adjacent sequences: A146560 A146561 A146562 * A146564 A146565 A146566

Keyword

hard,more,nonn

Author

Robert Smith (robert_smith44(AT)hotmail.com), Nov 01 2008

Status

approved