sequence A079490...
GerardS
Gerard at PrairieTech.Net
Wed Jan 22 23:25:03 CET 2003
Hugo Pfoertner wrote:
I have only 33 digits accuracy with VAX quadruple precision, but that is
sufficient
to exclude 62 from the sequence. With
C A079490
INTEGER ARG
REAL*16 QARG, EX, DIFF, DIFMIN
DIFMIN = 100.0Q0
DO 10 ARG = 1, 76
QARG = QEXT ( ARG )
EX = QEXP(QARG)
DIFF = EX - QNINT(EX)
IF ( QABS(DIFF) .LT. DIFMIN ) THEN
DIFMIN = QABS(DIFF)
WRITE (*,*) ARG, DIFF
ENDIF
10 CONTINUE
END
I get:
1 -0.281718171540954764639712528647338
3 8.553692318766774092852965458171901E-0002
8 -4.201295827172525640790054711137231E-0002
19 -3.681273915508996621127729387694541E-0002
45 3.479723340609908177611941937357187E-0002
75 0.000000000000000000000000000000000E+0000
on my Digital Alphastation
Mark Hudson wrote:
I have a question about sequence A079490.
ID Number: A079490
Sequence: 1,3,8,19,45,62
Name: Exp(n) is closer to an integer than any previous exp(k) for 1 <=
k < n.
Example: a(2) = 3, exp(3) = 20.08... is closer to an integer than exp(1) =
2.718...
Program: (PARI) d=1; for( n=1,500, x=exp(n); y=1/(( x-floor(x)) *
(ceil(x)-x)) ; if( y>d, print( n); d= y, ))
I was thinking of extending the sequence when I ran into a question.
The terms I get are:
1,3,8,19,45,75,135,178,209,732,...
so my sequence diverges from the one in the database after term=45.
If my understanding of the definition of the sequence is correct, then I
should look at the fractional parts of exp(n) for each term:
frac(exp(45)) = 0.03479...
frac(exp(62)) = 0.0373...
frac(exp(75)) = 0.01434...
Although I may have missed a term before 75 which is closer to its nearest
integer than 45 is, since exp(62)) is further from an integer than exp(45)
is, I do not see that this can be the next term in the sequence after 45.
Mark.
GerardS wrote:
I wrote a simple REXX program that had 1000 digits (decimal) of accuracy.
I found that 62 wasn't in the sequence, and 732 was the last before 1,111.
I'll run the program overnight to 10,001 and see what comes out.
_________________________________________________________________Gerard S.
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