

A093439


Least number n with a given prime signature such that all numbers >= n with this prime signature are one less than a composite number.


1



3, 8, 9, 32, 64, 81, 128, 216, 512, 1024, 1728, 2048, 4096, 6561, 7776, 8192, 13824, 16384, 27000, 32768, 46656, 110592, 131072, 216000, 248832, 262144, 279936, 373248, 524288, 884736, 1048576, 1728000, 2097152, 2985984, 4194304, 5832000
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OFFSET

1,1


COMMENTS

This is to categorize prime signatures such that p^a*q^b*r^c ... +1 is composite, p,q,r are arbitrarily chosen primes. Example: Perfect odd powers + 1 is always composite. Are there other examples? Exceptions like 3 and 5 are to be ignored.


LINKS

Table of n, a(n) for n=1..36.


EXAMPLE

8 = 2^3 is a member as 8 has a prime signature p^3 and all numbers of the form p^3+1 are composite.
9 is also a member though 2^2+1 = 5 is a prime but for all odd primes p^2+1 is even.
216 = 2^3*3^3 is a member because p^3*q^3+1 is always divisible by pq+1.


CROSSREFS

Cf. A093438.
Sequence in context: A297324 A223331 A101720 * A000927 A055513 A038226
Adjacent sequences: A093436 A093437 A093438 * A093440 A093441 A093442


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Apr 01 2004


EXTENSIONS

More terms from David Wasserman, Sep 12 2006


STATUS

approved



