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A137411
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Weak Goodstein sequence starting at 11.
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13
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11, 30, 67, 127, 217, 343, 511, 636, 775, 928, 1095, 1276, 1471, 1680, 1903, 2139, 2389, 2653, 2931, 3223, 3529, 3849, 4183, 4531, 4893, 5269, 5659, 6063, 6481, 6913, 7359, 7818, 8291, 8778, 9279, 9794, 10323, 10866, 11423, 11994, 12579, 13178
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OFFSET
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2,1
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COMMENTS
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The sequence eventually goes to zero, as can be seen by noting that multiples of the highest exponent (3 in this case) only go down; in fact the 8th term, a(8) = 7*8^2 + 7*8 + 7 = 511; after which the multiple of the square term will only go down, etc.
This sequence, for 11, grows beyond the quintillions of digits before going to zero.
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REFERENCES
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K. Hrbacek & T. Jech, Introduction to Set Theory, Taylor & Francis Group, 1999, pp. 125-127.
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LINKS
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FORMULA
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To obtain a(n + 1), write a(n) in base n, increase the base to n + 1 and subtract 1.
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EXAMPLE
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a(2) = 11 = 2^3 + 2^1 + 2^0
a(3) = 3^3 + 3^1 + 3^0 - 1 = 30
a(4) = 4^3 + 4^1 - 1 = 4^3 + 3*4^0 = 67
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MATHEMATICA
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nxt[{n_, a_}]:={n+1, FromDigits[IntegerDigits[a, n+1], n+2]-1}; Transpose[ NestList[ nxt, {1, 11}, 50]][[2]] (* Harvey P. Dale, Feb 09 2015 *)
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CROSSREFS
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Cf. A056004 (strong Goodstein sequences), A059933 (strong Goodstein sequence for 16.).
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KEYWORD
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nonn
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AUTHOR
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Nicholas Matteo (kundor(AT)kundor.org), Apr 15 2008
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STATUS
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approved
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