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Search: id:A097398
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| A097398 |
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Matrix T(m,x(1)), m>=1, x(1)>=2, read by anti-diagonals, 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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3
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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
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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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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Eric Weisstein's World of Mathematics: Goebel's Sequence.
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EXAMPLE
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T(m,x(1))=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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Cf. A003504 for more references and links, A005166, A005167.
Sequence in context: A107814 A093762 A156677 this_sequence A033363 A127147 A051614
Adjacent sequences: A097395 A097396 A097397 this_sequence A097399 A097400 A097401
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KEYWORD
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nonn,tabl
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Aug 15 2004
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EXTENSIONS
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m=10 row corrected by Don Reble, Dec 07 2004. He remarks that the versions in the books of Ibstedt and Guy are both wrong.
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