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A359450
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a(1) = 1, a(2) = 2; thereafter a(n) = n * a(A070939(n)).
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2
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1, 2, 6, 24, 30, 36, 42, 192, 216, 240, 264, 288, 312, 336, 360, 480, 510, 540, 570, 600, 630, 660, 690, 720, 750, 780, 810, 840, 870, 900, 930, 1152, 1188, 1224, 1260, 1296, 1332, 1368, 1404, 1440, 1476, 1512, 1548, 1584, 1620, 1656, 1692, 1728, 1764, 1800, 1836
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OFFSET
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1,2
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COMMENTS
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Problem A6 of the 63rd Putnam Competition (2002) asked to prove that when this sequence is generalized to base-b digits, the sum of reciprocals converges only for b = 2.
Problem 2 in Appendix D of Bornemann et al. (2004) asked to calculate the sum of the reciprocals of this sequence.
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REFERENCES
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Daniel D. Bonar and Michael J. Khoury, Jr., Real infinite Series, The Mathematical Association of America, 2006, pp. 159, 190-191.
Hongwei Chen, Classical Analysis: An Approach through Problems, CRC Press, 2022, p. 118, exercise 34.
Kiran S. Kedlaya, Daniel M. Kane, Jonathan M. Kane, and Evan M. O'Dorney, The William Lowell Putnam Mathematical Competition 2001-2016: Problems, Solutions, and Commentary, American Mathematical Society, 2020, pp. 86-87.
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LINKS
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Folkmar Bornemann, Dirk Laurie, Stan Wagon, and Jörg Waldvogel, The SIAM 100-Digit Challenge, A Study in High-Accuracy Numerical Computing, SIAM, Philadelphia, 2004. See Appendix D, Problem 2, p. 281.
John Scholes, Problem A6, The 63rd Putnam Competition, 2002.
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FORMULA
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MATHEMATICA
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a[1] = 1; a[2] = 2; a[n_] := a[n] = n * a[BitLength[n]]; Array[a, 100]
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PROG
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(PARI) a(n) = if(n < 3, n, n * a(#binary(n)));
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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