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Search: id:A000959
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| A000959 |
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Lucky numbers.
(Formerly M2616 N1035)
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+0
196
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| 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99, 105, 111, 115, 127, 129, 133, 135, 141, 151, 159, 163, 169, 171, 189, 193, 195, 201, 205, 211, 219, 223, 231, 235, 237, 241, 259, 261, 267, 273, 283, 285, 289, 297, 303
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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An interesting general discussion of the phenomenon of 'random primes' (generalizing the lucky numbers) occurs in Hawkins (1958). Heyde (1978) proves that Hawkins' random primes do not only almost always satisfy the Prime Number Theorem but also the Riemann Hypothesis. - Alf van der Poorten, Jun 27 2002
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REFERENCES
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M. Gardner, Lucky numbers and 2187, Math. Intellig., 19 (No. 2, 1997), 26-29.
M. Gardner, Gardner's Workout, Chapter 21 "Lucky Numbers and 2187" pp. 149-156 A. K. Peters MA 2002.
V. Gardiner, R. Lazarus, N. Metropolis and S. Ulam, On certain sequences of integers defined by sieves, Math. Mag., 29 (1955), 117-119.
R. K. Guy, Unsolved Problems in Number Theory, C3.
D. Hawkins, The random sieve, Math. Mag. 31 (1958), 1-3.
D. Hawkins and W. E. Briggs, The lucky number theorem. Math. Mag. 31 1958 81-84.
C. C. Heyde, Ann. Probability, 6 (1978), 850-875.
C. S. Ogilvy, Tomorrow's Math. 2nd ed., Oxford Univ. Press, 1972, p. 99.
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 114.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
I. Peterson, MathTrek, Martin Gardner's Lucky Numbers
I. Peterson, See also
W. Schneider, Lucky Numbers [Broken link?]
T. Sillke, S.M.Ulam's Lucky Numbers
G. Villemin's Almanach of Numbers, Nombre Chanceux
Eric Weisstein's World of Mathematics, Lucky number.
Wikipedia, Lucky number
Index entries for "core" sequences
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FORMULA
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Delete every 2nd number, leaving 1 3 5 7 ...; the 2nd number remaining is 3, so delete every 3rd number, leaving 1 3 7 9 13 15 ...; now delete every 7th number, leaving 1 3 7 9 13 ...; now delete every 9th number; etc.
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MATHEMATICA
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t = 2Range@200 - 1; f[n_] := Block[{k = t[[n]]}, t = Delete[t, Table[{k}, {k, k, Length@t, k}]]]; Do[f@n, {n, 2, 30}]; t (from Robert G. Wilson v (rgwv(at)rgwv.com), May 09 2006)
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CROSSREFS
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Cf. A137164-A137185.
Adjacent sequences: A000956 A000957 A000958 this_sequence A000960 A000961 A000962
Sequence in context: A032678 A073671 A024901 this_sequence A120226 A137310 A118567
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KEYWORD
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nonn,easy,nice,core
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AUTHOR
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njas. Entry updated Mac 07 2008
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