|
| |
|
|
A072665
|
|
Center of smallest run of 2n+1 consecutive numbers with exactly n+1,n,...,2,1,2,...,n,n+1 distinct prime factors, respectively.
|
|
1
| | |
|
|
|
OFFSET
| 0,1
|
|
|
COMMENTS
| Borrowing from musical terminology, these could be considered "swells" of primality - first a crescendo ("more prime"), then a decrescendo ("less prime"). a(4), if it exists, is greater than 70750000. The corresponding sequence but counting prime factors with multiplicity (A01222) cannot exist because either the number immediately before or after the odd center would be a multiple of 4, thus would always have to be 4.
|
|
|
EXAMPLE
| a(0) = 2 (prime) is the smallest number with one prime factor. a(1) = 11 as 10 (=2*5), 11 (prime) and 12 (=2^2*3) have 2,1,2 distinct prime factors (A01221), respectively and there is no smaller center of such a run. a(2) = 2917 as 2915 (=5*11*53), 2916 (=2^2*3^6), 2917 (prime), 2918 (=2*1459) and 2919 (=3*7*139) have 3,2,1,2,3 distinct prime factors and there is no smaller such run.
|
|
|
CROSSREFS
| Cf. A072664 (smallest finish with run pattern n, ..., 2, 1), A072663 (smallest start with run pattern 1, 2, ..., n), A001221 (omega).
Sequence in context: A101295 A131306 A145797 * A201264 A087344 A027736
Adjacent sequences: A072662 A072663 A072664 * A072666 A072667 A072668
|
|
|
KEYWORD
| hard,nonn,bref
|
|
|
AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jul 30 2002
|
| |
|
|
