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.

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

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 3,4,5 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: A298747 A327105 A356451 * A349536 A038673 A183219

Adjacent sequences: A129615 A129616 A129617 * A129619 A129620 A129621

Keyword

nonn,uned

Author

J. M. Bergot, May 30 2007

Status

approved