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 A225852 The number of people required for there to be at least a 50% chance that at least 3 share a birthday in a year with n days. 4
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 OFFSET 1,1 COMMENTS a(365) = 88. For n <= 1000, a(n) = 1.436 + 1.812*n^0.654 - 0.817/n^3 provides an estimate accurate to 0.6 units. LINKS Christian N. K. Anderson, Table of n, a(n) for n = 1..1000 Christian N. K. Anderson, Table of n and exact probabilities of a(n)-1 and a(n) for n = 1..1000 P. Le Conte, Coincident Birthdays EXAMPLE The probability that out of 87 people 3 share a birthday in a year with 365 days is 0.4994549. The corresponding probability for 88 people is 0.5110651. Therefore a(365)=88. PROG (R) library(gmp); #prob of a maximum of exactly k coincident birthdays is BigQ<-function(nday, p, k) { #nday=days in a year; p=people     if(p1, sum(sapply(2:k-1, function(j) BigQ(nday-i, p-k*i, j))), 1)     }     tot } BDaySharedByAtLeast<-function(nday, people, k) {     if(nday<1 | people

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)