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Search: id:A129618
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| A129618 |
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A method of using three consecutive coprimes to generate numbers either one away from a prime or splitting two twin primes. The sequence lists the first of a group of three coprimes. |
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+0
1
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| 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 31, 33, 34, 35, 36, 38, 39, 40, 42, 44, 46, 47, 48, 49, 50
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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In 50 trials of trios of consecutive coprimes, nine failed to be within one of a prime; four split twin primes; and 37 were within one of a prime. The results were 37 + 2x4 = 45 prime neighbors from 50 trials. Does this sequence continue to produce primes with a probability greater than mere chance?
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FORMULA
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The first group is 1,2,3; the 2nd is 2,3,5; the 3rd is 4,5,7 and so forth as the first number increases by one. Place a group of three coprimes a,b and c into a^2 + b^2 + c to see how close the sum comes to a prime.
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EXAMPLE
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Take 12,13,17 to yield 12^2 + 13^2 + 17 = 144+169+17=330 which
is one away from the prime 331.
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CROSSREFS
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Sequence in context: A097502 A064364 A004726 this_sequence A038673 A049533 A052419
Adjacent sequences: A129615 A129616 A129617 this_sequence A129619 A129620 A129621
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KEYWORD
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nonn,uned
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AUTHOR
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J. M. Bergot (thekingfishb(AT)yahoo.ca), May 30 2007
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