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Search: id:A113295
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| A113295 |
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Prime differences of Lucas 4-step numbers. |
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+0
2
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| 3, 11, 19, 23, 47, 73, 701, 1361, 4363, 9067, 9749, 17477, 18743, 18839, 36293, 70003, 116101, 134917, 366437, 465061, 498749, 501013, 1844033, 3590099, 13305307, 13341259, 13341619, 36229121, 49069367, 49570721, 95550661, 351427309
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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These are primes from the sequence A113294, which is differences of Lucas 4-step numbers, also known as "Tetranacci Lucas numbers" or "Tetranacci numbers with different initial conditions" in A073817. Also in the difference set sequence are: 13340261 = 11 * 19 * 29 * 31 * 71 is a product of 5 distinct 2-digit primes; 95550683 = 269 * 593 * 599 is a product of 3 distinct 3-digit primes.
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LINKS
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Eric Weisstein's World of Mathematics, Lucas n-Step Number.
Noe, T. D. and Post, J. V., Primes in Fibonacci n-step and Lucas n-Step Sequences." J. Integer Seq. 8, Article 05.4.4, 2005.
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FORMULA
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{a(n)} = Intersection of { | A073817(i) - A073817(j) | such that i>=j} and A000040. {a(n)} = Prime elements of { | A073817(i) - A073817(j) | such that i>=j}. {a(n)} = Prime elements of A113294.
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EXAMPLE
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a(1) = 3 because A073817(0)-A001644(1) = 4 - 1 = 3, a prime.
a(2) = 11 because A073817(4)-A001644(0) = 15 - 4 = 11, a prime.
a(3) = 19 because A073817(5)-A001644(3) = 26 - 7 = 19, a prime.
a(4) = 23 because A073817(5)-A001644(2) = 26 - 3 = 23, a prime.
a(16) = 70003 because A073817(17)-A001644(0) = 70007 - 4 = 70003, a prime.
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CROSSREFS
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Cf. A000040, A073817, A113188-A113194, A113238, A113239, A113244, A113293, A113294.
Sequence in context: A030377 A092060 A071916 this_sequence A043433 A078583 A017101
Adjacent sequences: A113292 A113293 A113294 this_sequence A113296 A113297 A113298
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 23 2005
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