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A131354
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Number of primes in the open interval between successive tribonacci numbers.
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1
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0, 0, 0, 0, 1, 1, 1, 3, 5, 8, 12, 23, 38, 61, 109, 179, 312, 537, 920, 1598, 2779, 4835, 8461, 14784, 25984, 45696
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| This is to tribonacci numbers A000073 as A052011 is to Fibonacci numbers and as A052012 is to Lucas numbers A000204. It is mere coincidence that all values until a(12) = 38 are themselves Fibonacci. The formula plus the known asymptotic prime distribution gives the asymptotic approximation of this sequence, which is the same even if we use one of the alternative definitions of tribonacci with different initial values.
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FORMULA
| a(n) = A000720(A000073(n+1)) - A000720(A000073(n)), if both A000073 are nonprime.
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EXAMPLE
| Between Trib(8)=24 and Trib(9)=44 we find the following primes: 29, 31, 37, 41, 43, hence a(8)=5.
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MAPLE
| A131354 := proc(n)
a := 0 ;
for k from 1+A000073(n) to A000073(n+1)-1 do
if isprime(k) then
a := a+1 ;
end if;
end do;
a ;
end proc: # R. J. Mathar, Dec 14 2011
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CROSSREFS
| Cf. A000073, A092836, A052011, A052012, A056816.
Sequence in context: A147879 A147880 A020643 * A092360 A129141 A097431
Adjacent sequences: A131351 A131352 A131353 * A131355 A131356 A131357
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 21 2007
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