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A097398
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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).
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5
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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
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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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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STATUS
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approved
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