WOLFRAM|DEMONSTRATIONS PROJECT

Lucky Numbers

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sieve step
5
sequence size
601
view
sieve
array plot
differences plot
list plot
number of prime twins: 32
number of luckies that differ by two: 48
number of primes less than 601: 110
number of luckies less than 601: 143
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Around 1955, Stanislaw Ulam identified the lucky number sequence, 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, …. Start with the odd numbers 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, … and keep 1 in the sequence. The next number is 3; strike out every third number from the beginning, so that the sequence is 1, 3, 7, 9, 13, 15, 19, 21, …. This strikes out 5, 11, 17, 23, and so on. The next number left is 7; strike out every seventh integer from the beginning of the last sequence to get 1, 3, 7, 9, 13, 15, 21, …, which strikes out 19, …. The integers that are left are shown highlighted in yellow.