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A359450
a(1) = 1, a(2) = 2; thereafter a(n) = n * a(A070939(n)).
2
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
OFFSET
1,2
COMMENTS
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.
REFERENCES
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.
LINKS
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.
Kiran Kedlaya and Lenny Ng, Solutions to the 63rd William Lowell Putnam Mathematical Competition, Saturday, December 7, 2002. See Problem A-6, p. 2.
Leonard F. Klosinski, Gerald L. Alexanderson, and Loren C. Larson, The Sixty-Third William Lowell Putnam Mathematical Competition, The American Mathematical Monthly, Vol. 110, No. 8 (2003), pp. 718-726.
John Scholes, Problem A6, The 63rd Putnam Competition, 2002.
David Smith, On a slowly converging sum, Solution to Problem 2, 2003.
FORMULA
Sum_{n>=1} 1/a(n) = A359451.
MATHEMATICA
a[1] = 1; a[2] = 2; a[n_] := a[n] = n * a[BitLength[n]]; Array[a, 100]
PROG
(PARI) a(n) = if(n < 3, n, n * a(#binary(n)));
CROSSREFS
Sequence in context: A079433 A319205 A110728 * A190424 A322484 A066332
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Jan 02 2023
STATUS
approved