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Search: id:A127014
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| A127014 |
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a(n) = smallest k such that A(k) == 0 mod 2^n, where A(0) = 1 and A(k) = k*A(k-1) + 1 = A000522(k). |
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3
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| 1, 3, 3, 3, 19, 51, 115, 115, 115, 627, 627, 2675, 2675, 2675, 2675, 35443, 35443, 166515, 166515, 166515, 1215091, 3312243, 3312243, 3312243, 3312243, 36866675
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n+1) - a(n) = 2^n or 0; see A127015.
In the 2-adic integers, lim_{n->infty} a(n) = 11001110010100010100110001...; see A127015.
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REFERENCES
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N. Koblitz, p-adic Numbers, p-adic Analysis and Zeta-Functions, 2nd ed., Springer, New York, 1996.
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LINKS
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J. Sondow, Which Partial Sums of the Taylor Series for e Are Convergents to e? (and a Link to the Primes $2, 5, 13, 37, 463, ...$) with an Appendix "Periodic Behaviour of Some Recurrence Sequences Related to $e$, Modulo Powers of 2" by Kyle Schalm
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FORMULA
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A(a(n)) = A138761(n) = Sum_{k=0...a(n)} a(n)!/k! for n > 0. [From Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Jun 12 2009]
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EXAMPLE
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A(0) = 1, A(1) = 2, A(2) = 5 and A(3) = 16 = 2^4, so a(1) = 1 and a(2) = a(3) = a(4) = 3. Also, A(19) = 330665665962404000 is the first A(k) divisible by 2^5, so a(5) = 19.
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CROSSREFS
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Cf. A000522, A127015.
Cf. A138761. [From Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Jun 12 2009]
Sequence in context: A110668 A083562 A106542 this_sequence A073748 A131445 A033874
Adjacent sequences: A127011 A127012 A127013 this_sequence A127015 A127016 A127017
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KEYWORD
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nonn
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AUTHOR
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Kyle Schalm (kschalm(AT)math.utexas.edu), Jan 07 2007
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