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Search: id:A073593
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| A073593 |
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Number of cards needed to be drawn (with replacement) from a deck of n cards to have a 50% or greater chance of seeing each card at least once. |
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+0
3
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| 1, 2, 5, 7, 10, 13, 17, 20, 23, 27, 31, 35, 38, 42, 46, 51, 55, 59, 63, 67, 72, 76, 81, 85, 90, 94, 99, 104, 108, 113, 118, 123, 128, 133, 137, 142, 147, 152, 157, 162, 167, 173, 178, 183, 188, 193, 198, 204, 209, 214, 219, 225, 230, 235, 241, 246, 251, 257, 262
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A version of the coupon collector's problem.
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REFERENCES
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A question posted to sci.math Aug 19 2002 06:35:47 PST by Colgathar (colgathar(AT)yahoo.com) titled "Collecting a deck of cards on the street." with analysis by Kevin Buhr (buhr(AT)telus.net), Michael Press (prezky(AT)apple.com) & DMB (nospamplease(AT)starpower.net).
W. Feller, An Introduction to Probability Theory and Its Applications: Volume 1.
Ross, "A First Course in Probability" (3rd ed., chapter 7, example 3g).
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FORMULA
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a(n) seems to be asymptotic to n*(log(n)+c) with c=0.3(6)...and maybe c=1/e. - Benoit Cloitre, Sep 07, 2002
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MATHEMATICA
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f[n_] := Block[{k = 1}, While[2StirlingS2[k, n]*n!/n^k < 1, k++ ]; k]; Table[ f[n], {n, 1, 60}]
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PROGRAM
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(PARI) S2(n, k) = if(k<1|k>n, 0, if(n==1, 1, k*S2(n-1, k)+S2(n-1, k-1))); a(n)=if(n<0, 0, k=1; while( 2*S2(k, n)*n!/n^k<1, k++); k)
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CROSSREFS
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Sequence in context: A057347 A067008 A094065 this_sequence A088947 A071113 A071704
Adjacent sequences: A073590 A073591 A073592 this_sequence A073594 A073595 A073596
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 28 2002
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