|
| |
|
|
A143700
|
|
a(n) = least odd number m minimizing A007947(m(2^n-m))
|
|
8
|
|
|
|
1, 1, 1, 1, 5, 1, 3, 13, 169, 25, 243, 375, 11, 49, 7, 3, 18225, 71875, 4913, 1701, 144027, 1825, 3483, 2197, 9156027, 131989, 1103, 5103, 38525, 458703, 1523, 3483891, 19283525
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,5
|
|
|
COMMENTS
|
Smallest odd number a(n) such that product of distinct prime divisors of (2^n)*a(n)*(2^n-a(n)) is the smallest available for a(n)<=2^x-a(n)<2^x.
Product of distinct prime divisors of (2^n)*a(n)*(2^n-a(n)) is called also radical: rad((2^n)*a(n)*(2^n-a(n))
For numbers 2^n-a(n) see A143701
For minimal values of rad((2^n)*a(n)*(2^n-a(n)) see A143702
Related to the abc conjecture. [From M. F. Hasler, Nov 13 2008]
|
|
|
LINKS
|
Table of n, a(n) for n=1..33.
|
|
|
MATHEMATICA
|
a = {{1, 1}}; aa = {1}; bb = {}; rr = {}; Do[logmax = 0; k = 2^x; w = Floor[(k - 1)/2]; Do[m = FactorInteger[n (k - n)]; rad = 1; Do[rad = rad m[[s]][[1]], {s, 1, Length[m]}]; log = Log[k]/Log[rad]; If[log > logmax, bmin = k - n; amax = n; logmax = log; r = rad], {n, 1, w, 2}]; Print[{x, amax}]; AppendTo[aa, amax]; AppendTo[bb, bmin]; AppendTo[rr, r]; AppendTo[a, {x, logmax}], {x, 2, 15}]; aa (*Artur Jasinski with assistance of Maximilian Hasler*)
|
|
|
PROG
|
(PARI) A143700(n)={ local(b=1, m=2^n-b); forstep(a=3, 2^(n-1), 2, A007947(a)*A007947(2^n-a)<m|next; m=A007947((2^n-a)*b=a)); b } [From M. F. Hasler, Nov 13 2008]
|
|
|
CROSSREFS
|
A007947, A085152, A085153, A147298-A147307, A147638-A147643.
Sequence in context: A074048 A176321 A134894 * A036790 A201847 A185559
Adjacent sequences: A143697 A143698 A143699 * A143701 A143702 A143703
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Artur Jasinski, Nov 10 2008
|
|
|
EXTENSIONS
|
a(28)-a(33) & PARI code from M. F. Hasler, Nov 13 2008
|
|
|
STATUS
|
approved
|
| |
|
|
