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A276309
Integer part of the ratio of alternate consecutive prime gaps.
7
2, 2, 1, 1, 1, 1, 3, 0, 1, 2, 0, 1, 3, 1, 0, 1, 2, 0, 1, 2, 1, 2, 0, 0, 1, 1, 1, 7, 1, 0, 0, 1, 1, 0, 3, 0, 1, 1, 0, 1, 1, 0, 1, 3, 6, 0, 0, 1, 3, 0, 1, 3, 0, 1, 0, 1, 2, 0, 2, 7, 0, 0, 1, 7, 1, 0, 0, 0, 3, 2, 1, 0, 0, 1, 2, 0, 1, 2, 0, 1, 1, 0, 2, 1, 2, 0, 0, 1, 6, 2, 0, 1, 1, 0, 3, 0
OFFSET
1,1
COMMENTS
Conjectures: The most frequent ratio among alternate prime gaps is 1, while the most frequent ratios among consecutive prime gaps seems to be 2 and 1/2, both with nearly the same frequency (see links). It also appears that next four most frequent ratios are 2, 1/2, 3 and 1/3, all four with nearly the same frequency (see links).
FORMULA
a(n) = floor((prime(n + 3) - prime(n + 2))/(prime(n + 1) - prime(n))) .
EXAMPLE
For n=2, the second prime is 3, and the next three primes are 5, 7, and 11. So the ratio of prime gaps is (11-7)/(5-3) = 4/2 = 2, and the integer part of this is a(2) = 2. - Michael B. Porter, Aug 11 2016
MATHEMATICA
Table[Floor[(Prime[j + 3] - Prime[j + 2])/(Prime[j + 1] - Prime[j])], {j, 1, 200}]
PROG
(Magma) [Floor((NthPrime(n+3)-NthPrime(n+2))/(NthPrime(n+ 1)- NthPrime(n))): n in [1..100]]; // Vincenzo Librandi, Aug 30 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Andres Cicuttin, Aug 06 2016
STATUS
approved