login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A097398 Matrix T(m,x(1)), m>=1, x(1)>=2, read by antidiagonals, where T(m,x(1)) gives the position of the first noninteger term in the sequence defined by x(n)=(x(n-1)*(x(n-1)^m+n-1))/n for n>=2 with exponent m and the given starting value x(1). 4
43, 7, 89, 17, 89, 97, 34, 89, 17, 214, 17, 89, 23, 43, 19, 17, 31, 97, 139, 83, 239, 51, 151, 149, 107, 13, 191, 37, 17, 79, 13, 269, 19, 359, 7, 79, 7, 89, 13, 107, 13, 419, 23, 127, 83, 34, 79, 83, 214, 37, 127, 37, 158, 31, 239 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The rectangular table (Table 1, page 35) in Ibstedt's book gives the position of the first noninteger term for parameters x1 and m:

  m\x1: 2   3   4   5   6   7   8   9  10  11

   1   43   7  17  34  17  17  51  17   7  34

   2   89  89  89  89  31 151  79  89  79 601

   3   97  17  23  97 149  13  13  83  23  13

   4  214  43 139 107 269 107 214 139 251 107

   5   19  83  13  19  13  37  13  37 347  19

   6  239 191 359 419 127 127 239 191 239 461

   7   37   7  23  37  23  37  17  23   7  37

   8   79 127 158  79 103 103 163 103 163  79

   9   83  31  41  83  71  83  71  23  41  31

  10  239 389 169 137 239 239 239 239 239 389

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, E15.

Henry Ibstedt, Mainly natural numbers - a few elementary studies on Smarandache sequences and other number problems, Henry Ibstedt. - Martinsville, Ind.: Bookman, 2003. Chapter IV, Some Sequences of Large Integers, pp. 32-37.

LINKS

Table of n, a(n) for n=1..55.

H. Ibstedt, Some sequences of large integers, Fibonacci Quart. 28 (1990), 200-203

Eric Weisstein's World of Mathematics: Göbel's Sequence

EXAMPLE

T(1,3)=a(2)=7: x(1)=3, x(2)=x(1)*(x(1)^1+2-1)/n=3*(3+2-1)/2=6, x(3)=6*(6+3-1)/3=16, x(4)=16*(16+4-1)/4=76, x(5)=76*(76+5-1)/5=1216, x(6)=1216*(1216+6-1)/6=247456, x(7)=247456*(247456+7-1)/7=8747993810+2/7; i.e., x(7) is the first noninteger term in the sequence x(n) = x(n-1)*(x(n-1)^1+n-1)/n, n>=2, x(1)=3.

CROSSREFS

Cf. A003504 for more references and links, A005166, A005167.

Sequence in context: A107814 A093762 A156677 * A225210 A033363 A187088

Adjacent sequences:  A097395 A097396 A097397 * A097399 A097400 A097401

KEYWORD

nonn,tabl

AUTHOR

Hugo Pfoertner, Aug 15 2004

EXTENSIONS

m=10 row corrected by Don Reble, Dec 07 2004, who remarks that the versions in the books of Ibstedt and Guy are both wrong

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 23 01:10 EDT 2019. Contains 326211 sequences. (Running on oeis4.)