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Search: id:A152577
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| A152577 |
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Numbers of the form 10^(2k+1) + 1. |
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+0
1
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| 11, 1001, 100001, 10000001, 1000000001, 100000000001, 10000000000001, 1000000000000001, 100000000000000001, 10000000000000000001, 1000000000000000000001, 100000000000000000000001
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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These numbers are all divisible by 11. This follows from the identity
a^n-b^n = (a+b)(a^(n-1) - a^(n-2)b + ... + b^(n-1)) for odd values of n. In
this example a=10 and b=1 so a+b = 11. The sum of digits rule for divisibility
by 11 also applies.
Bisection of A000533. Also, bisection of A062397. a(n) is also A084508(n+1) written in base 2. a(n) is also A087289(n-1) written in base 2. a(n) is also the concatenation of "1", 2(n-1) digits "0" and "1". [From Omar E. Pol (info(AT)polprimos.com), Dec 13 2008]
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EXAMPLE
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Contribution from Omar E. Pol (info(AT)polprimos.com), Dec 14 2008: (Start)
n ....... a(n)
1 ....... 11
2 ...... 1001
3 ..... 100001
4 .... 10000001
5 ... 1000000001
(End)
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PROGRAM
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(PARI) g(n)=forstep(x=1, n, 2, y=(10^x+1); print1(y", "))
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CROSSREFS
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Cf. A000533, A062397, A084508, A087289. [From Omar E. Pol (info(AT)polprimos.com), Dec 13 2008]
Sequence in context: A083816 A004656 A143016 this_sequence A163449 A127961 A127962
Adjacent sequences: A152574 A152575 A152576 this_sequence A152578 A152579 A152580
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), Dec 08 2008
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