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Search: id:A117085
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| A117085 |
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Decimal value of binary number whose n-th 1 is followed by L(n) 0's. |
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+0
1
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| 9, 37, 593, 18977, 4858113, 19898830849, 10432718228160513, 11202045899583117393395713, 3153095608696857509125380749498911817729, 476482336633392067336089761008918511215119000704844672205324289
(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 Lucas numbers as A117067 "Decimal value of binary number whose n-th 1 is followed by F(n) 0's" is to Fibonacci numbers. Primes include a(2) = 37 and a(3) = 593.
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FORMULA
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a(0) = 0, for positive n: a(n+1) = 1 + a(n)*2^(1+L(n)) = 1 + a(n)*2^(1+A000032(n)).
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EXAMPLE
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a(1) = 9 because 1001 (base 2) = 1 + 2^(1+2) = 9 (base 10), where the two 0's correspond to L(1) = A000032(1) = 2.
a(2) = 37 because 100101 (base 2) = 1 + (1 + 2^(1+2))*2^(1+1) = 37 (base 10).
a(3) = 593 because 1001010001 (base 2) = 1 + (1 + (1 + 2^(1+2))*2^(1+1))*2^(1+3) = 593(base 10).
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CROSSREFS
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Cf. A000032, A117011, A117067, A117068.
Sequence in context: A048878 A026686 A076174 this_sequence A120780 A071229 A071238
Adjacent sequences: A117082 A117083 A117084 this_sequence A117086 A117087 A117088
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KEYWORD
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base,easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 17 2006
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