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Search: id:A104411
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| A104411 |
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Number of prime factors, with multiplicity, of the tetranacci numbers A000078. |
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+0
6
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| 0, 0, 1, 2, 3, 2, 1, 4, 5, 5, 1, 1, 3, 4, 6, 2, 2, 8, 5, 9, 2, 2, 4, 5, 6, 4, 2, 7, 5, 8, 2, 4, 3
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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I am using a(-2)=a(-1)=a(0)=0, a(1)=1 here. Prime tribonacci numbers: a(3)=2, a(7)=29, a(11)=401, a(12)=773, ... Semiprime tribonacci numbers: a(4)=4, a(6)=15, a(16) = 10671 = 3 * 3557, a(17) = 20569 = 67 * 307, a(21) = 283953 = 3 * 94651, a(22) = 547337 = 7 * 78191, a(27) = 14564533 = 491 * 29663, a(31) = 201061985 = 5 * 40212397
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REFERENCES
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Marcellus E. Waddill, "Some Properties of the Tetranacci Sequence Modulo m", The Fibonacci Quarterly, 30.3 (1992) 232.
Marcellus E. Waddill, "The Tetranacci Sequence and Generalizations", The Fibonacci Quarterly, 30.1 (1992) 9
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LINKS
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Eric Weisstein's World of Mathematics, Tetranacci Number.
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FORMULA
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a(n) = A001222(A000078(n)). a(n) = bigomega(A000078(n)).
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EXAMPLE
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a(1)=a(2)=0 because the first two nonzero tetranacci numbers are both 1, which has zero prime divisors.
a(3)=1 because the 3rd nonzero tetranacci number is 2, a prime, with only one prime divisor.
a(4)=2 because the 4th nonzero tetranacci number is 4 = 2^2 which has (with multiplicity) 2 prime divisors (which happen to be equal).
a(5)=3 because the 5th nonzero tetranacci number is 8 = 2^3.
a(6)=2 the 6th nonzero tetranacci number is 15 = 3*5, a semiprime, with two prime divisors.
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CROSSREFS
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Cf. A000078, A001222.
Sequence in context: A129773 A105789 A076549 this_sequence A055101 A081316 A079893
Adjacent sequences: A104408 A104409 A104410 this_sequence A104412 A104413 A104414
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Mar 05 2005
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