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.

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

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