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A062405
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Sums of specific numbers when generating a type of triangle based on pi(x).
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0
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2, 2, 5, 5, 8, 16, 11, 13, 18, 19, 20, 28, 30, 37, 30, 39, 39, 57, 46, 44, 52, 64, 62, 75, 60, 71, 79, 85, 74, 83, 90, 88, 95, 100, 111, 96, 104, 105, 115, 144, 117, 125, 148, 126, 132, 143, 165, 165, 144, 160, 172, 161, 174, 194, 173, 194, 198, 174, 212, 200, 205
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OFFSET
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0,1
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LINKS
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FORMULA
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pi(x) denotes the number of prime numbers less than or equal to x. Starting with x = 2 take pi(2x) - pi(x). The numbers 1, 1, 2, 1, 2, 2, 2, 3, 4, 3, ... will be found. Now create a new sequence based on the number of repeats. 2, 1, 1, 3, 1, 1, 1, ... Arrange these in a triangle such that 2 is the first row; 1, 1 is the second row; 3, 1, 1 is the third row; 1, 1, 2, 1 is the fourth row; etc. taking one more term each time. Now take the sum of the numbers on each row and this interesting sequence is generated.
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EXAMPLE
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Example: The first number on the triangle is 2 because the number 1 is repeated twice in the sequence of pi(2x) - pi(x).
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Rory Kulz (entropix(AT)amnaria.com), Jul 08 2001
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EXTENSIONS
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STATUS
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approved
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