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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

%I

%S 43,7,89,17,89,97,34,89,17,214,17,89,23,43,19,17,31,97,139,83,239,51,

%T 151,149,107,13,191,37,17,79,13,269,19,359,7,79,7,89,13,107,13,419,23,

%U 127,83,34,79,83,214,37,127,37,158,31,239

%N 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).

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

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

%C 1 43 7 17 34 17 17 51 17 7 34

%C 2 89 89 89 89 31 151 79 89 79 601

%C 3 97 17 23 97 149 13 13 83 23 13

%C 4 214 43 139 107 269 107 214 139 251 107

%C 5 19 83 13 19 13 37 13 37 347 19

%C 6 239 191 359 419 127 127 239 191 239 461

%C 7 37 7 23 37 23 37 17 23 7 37

%C 8 79 127 158 79 103 103 163 103 163 79

%C 9 83 31 41 83 71 83 71 23 41 31

%C 10 239 389 169 137 239 239 239 239 239 389

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

%D 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.

%H H. Ibstedt, <a href="http://www.fq.math.ca/Scanned/28-3/ibstedt.pdf">Some sequences of large integers</a>, Fibonacci Quart. 28 (1990), 200-203

%H Eric Weisstein's World of Mathematics: <a href="http://mathworld.wolfram.com/GoebelsSequence.html">Göbel's Sequence</a>

%e 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.

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

%K nonn,tabl

%O 1,1

%A _Hugo Pfoertner_, Aug 15 2004

%E 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

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Last modified August 2 02:53 EDT 2021. Contains 346409 sequences. (Running on oeis4.)