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Search: id:A131698
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| A131698 |
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Cumulative concatenation of A000032 Lucas numbers (beginning at 2). |
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+0
1
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| 2, 21, 213, 2134, 21347, 2134711, 213471118, 21347111829, 2134711182947, 213471118294776, 213471118294776123, 213471118294776123199, 213471118294776123199322, 213471118294776123199322521
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This is to A000032 as A130774 is to A000204. Like these Lucas numbers, a(n) cycles even, odd, odd, even, odd, odd, ... a(n) is prime for n = 1, 5, and semiprime for n = 2, 3, 6, 14. No more prime nor semiprime values through n = 60, which has a 381 digit composite factor.
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FORMULA
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a(1) = 2; a(n+1) = Concatenate(a(n),A000032(n+1)).
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EXAMPLE
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Table of first 14 values, with factorizations:
n a(n) factors
1 2 prime
2 21 3 * 7 semiprime
3 213 3 * 71 semiprime
4 2134 2 * 11 * 97
5 21347 is prime
6 2134711 719 * 2969 semiprime
7 213471118 = 2 * 7 * 19 * 802523
8 21347111829 = 3 * 12743 * 558401
9 2134711182947 = 7 * 491 * 621097231
10 213471118294776 = 2^3 * 3^2 * 41 * 7349 * 9839987
11 213471118294776123 = 3 * 41 * 785903 * 2208335567
12 213471118294776123199 = 11 * 23 * 349 * 2417648598420967
13 213471118294776123199322 = 2 * 23 * 37 * 3929 * 6991 * 4566234789049
14 213471118294776123199322521 = 61950375139 * 3445840607353939 semiprime.
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CROSSREFS
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Cf. A000032, A000204, A130774.
Sequence in context: A008351 A037743 A037638 this_sequence A109684 A137287 A106412
Adjacent sequences: A131695 A131696 A131697 this_sequence A131699 A131700 A131701
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KEYWORD
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base,easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Sep 15 2007
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