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Search: id:A075158
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| A075158 |
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Prime factorization of n+1 encoded with the run lengths of binary expansion. |
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+0
5
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| 0, 1, 2, 3, 5, 4, 10, 7, 6, 11, 21, 8, 42, 20, 9, 15, 85, 12, 170, 23, 22, 43, 341, 16, 13, 84, 14, 40, 682, 19, 1365, 31, 41, 171, 18, 24, 2730, 340, 86, 47, 5461, 44, 10922, 87, 17, 683, 21845, 32, 26, 27, 169, 168, 43690, 28, 45, 80, 342, 1364, 87381, 39, 174762
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(2n) = 1 or 2 mod 4 and a(2n+1) = 0 or 3 mod 4 for all n > 1
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LINKS
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Index entries for sequences that are permutations of the natural numbers
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EXAMPLE
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a(1) = 1 as 2 = 2^1, a(2) = 2 (10 in binary) as 3 = 3^1 * 2^0, a(3) = 3 (11) as 4 = 2^2, a(4) = 5 (101) as 5 = 5^1 * 3^0 * 2^0, a(5) = 4 (100) as 6 = 3^1 * 2^1, a(8) = 6 (110) as 9 = 3^2 * 2^0, a(11) = 8 (1000) as 12 = 3^1 * 2^2, a(89) = 35 (100011) as 90 = 5^1 * 3^2 * 2^1, a(90) = 90 (1011010) as 91 = 13^1 * 11^0 * 7^1 * 5^0 * 3^0 * 2^0.
The binary expansion of a(n) begins from the left with as many 1's as is the exponent of the largest prime present in the factorization of n+1, and from then on follows runs of ej+1 zeros and ones alternatively, where ej are the corresponding exponents of the successively lesser primes (0 if that prime does not divide n+1).
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CROSSREFS
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Inverse of A075157. a(n) = A075160(n+1)-1. a(A006093(n)) = A000975(n). Cf. A059884.
Sequence in context: A069202 A100932 A064360 this_sequence A066417 A079521 A112060
Adjacent sequences: A075155 A075156 A075157 this_sequence A075159 A075160 A075161
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen Sep 13 2002
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