haiku primes

[Jon Awbrey]

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variant generalizations of the predicate haikuprime? : N -> B,
not to be confused with the posinteger fn haikuprime : N -> N
that gives the n'th haikuprime.

1. haikuprime_1?(k) iff prime?(k) and prime?(2k + nextprime(k))
2. haikuprime_2?(k) iff prime?(k) and prime?(3k + 2)
3. haikuprime_3?(k) iff prime?(k) and prime?(k(lastprime(k) + lastlastprime(k))
or haikuprime_3?(k) iff k = prime(j) and prime?(prime(j-2) + prime(j-1)prime(j))

the triple of adjacent primes (2, 3, 5) yields the prime 2 + 3*5 = 17, so 5 is haiku_3,
but (prime + prime*prime) = (odd + odd*odd) = even for every other case so 5 is unique.

shorter than my usual sequence ...

ja

Joshua Zucker wrote:
> 
> On 12/16/06, Jonathan Post <jvospost3 at gmail.com> wrote:
> > the fact that the number of syllables in a haiku is prime.
> 
> OK, then, how about this (silly!) sequence:
> "Haiku primes" are primes p such that p + nextprime(p) + p is also prime.
> For example, 5 is the canonical haiku prime because 5, 7, and 5 are
> all prime, and so is 5+7+5.
> 
> [Of course, there could be argument about where the 7 comes from: is
> it nextprime(p) or is it p+2 or is it some other function?  If it's
> p+2 then the sequence is already in OEIS as A023208]

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