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A113058
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a(1) = a(2) = a(3) = 1; for n>2, a(n+1) = a(n) + a(n-1) + a(n-2) iff a(n) is prime, else a(n+1) = a(n) + 1.
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1
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1, 1, 1, 2, 4, 5, 11, 20, 21, 22, 23, 66, 67, 156, 157, 380, 381, 382, 383, 1146, 1147, 1148, 1149, 1150, 1151, 3450, 3451, 3452, 3453, 3454, 3455, 3456, 3457, 10368, 10369, 31104, 31105, 31106, 31107, 31108, 31109, 31110, 31111, 31112, 31113
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| A sequence which is locally tribonacci at prime values. a(n) is prime for a(4) = 2, a(6) = 5, a(7) = 11, a(11) = 23, a(13) = 67, a(15) = 157, a(19) = 383, a(25) = 1151, a(33) = 3457, a(35) = 10369, a(53) = 31121, ... a(n) is a Fibonacci number for n = 1, 2, 3, 4, 6, 9, ...
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EXAMPLE
| a(4) = 2 because a(4-1) = 1 is not prime, so a(4) = a(3) + 1 = 2.
a(5) = 4 because a(5-1) = 2 is prime, so a(5) = a(4) + a(3) + a(2) = 2 + 1 + 1 = 4.
a(6) = 5 because a(6-1) = 4 is not prime, so a(6) = a(5) + 1 = 4 + 1 = 5.
a(7) = 11 because a(7-1) = 5 is prime, so a(7) = a(6) + a(5) + a(4) = 5 + 4 + 2 = 11.
a(8) = 20 because a(8-1) = 11 is prime, so a(8) = a(7) + a(6) + a(5) = 11 + 5 + 4 = 20.
21.
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CROSSREFS
| Cf. A000040, A000073, A000213, A001590, A113050, A113051, A113057.
Sequence in context: A192581 A095023 A049913 * A066145 A095022 A101961
Adjacent sequences: A113055 A113056 A113057 * A113059 A113060 A113061
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 13 2005
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