

A146563


First instance primecover Sierpinski bases.


0




OFFSET

2,1


COMMENTS

A primecover 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, socalled 2cover, 2 = 1st prime. Sequence generated for 2, 3, 5 7 and 11cover.


LINKS

Table of n, a(n) for n=2..6.
Exotic covers
Robert Gerbicz, Covering Sets


FORMULA

To generate a member of the series, it is required to discover the lowest 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 primecovers are 4*14^n + 1 (2cover), 2012*74^n + 1 (3cover), 84536206*339^n + 1 (5cover), unknown*2601^n + 1 (7cover), and unknown*32400^n + 1 (11cover).


PROG

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


CROSSREFS

Sequence in context: A205590 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



