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A129618 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. 0
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; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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?

LINKS

Table of n, a(n) for n=1..41.

FORMULA

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.

EXAMPLE

Take 12,13,17 to yield 12^2 + 13^2 + 17 = 144+169+17=330 which is one away from the prime 331.

CROSSREFS

Sequence in context: A004726 A298747 A327105 * A038673 A183219 A049533

Adjacent sequences:  A129615 A129616 A129617 * A129619 A129620 A129621

KEYWORD

nonn,uned

AUTHOR

J. M. Bergot, May 30 2007

STATUS

approved

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Last modified April 17 08:34 EDT 2021. Contains 343064 sequences. (Running on oeis4.)