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A059054
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Integers which can be written as (b^k+1)/(b+1) for positive integers b and k.
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1
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1, 3, 7, 11, 13, 21, 31, 43, 57, 61, 73, 91, 111, 133, 157, 171, 183, 205, 211, 241, 273, 307, 343, 381, 421, 463, 507, 521, 547, 553, 601, 651, 683, 703, 757, 813, 871, 931, 993, 1057, 1111, 1123, 1191, 1261, 1333, 1407, 1483, 1561, 1641, 1723, 1807, 1893
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| It seems that all values are odd. For (b^k+1)/(b+1) to be an integer, it seems k must be odd. 2=(0^0+1)/(0+1) has been excluded since neither b nor k would be positive.
When k is a composite, a(n) is a composite.
These numbers are in the form of 111...1 (k of 1s) base b. - Lei Zhou, Feb 08 2012
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LINKS
| H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
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EXAMPLE
| 43 is in the sequence since (2^7+1)/(2+1)=129/3=43; indeed also (7^3+1)/(7+1)=344/8=43.
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MATHEMATICA
| max = 44; maxdata = (1 + max^3)/(1 + max); a = {}; Do[i = 1; While[i = i + 2; cc = (1 + m^i)/(1 + m); cc <= maxdata, a = Append[a, cc]], {m, 2, max}]; Sort[DeleteDuplicates[a]] (* Lei Zhou, Feb 08 2012 *)
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CROSSREFS
| Cf. A007583, A002061, A059055.
Sequence in context: A176797 A078098 A154831 * A197318 A109492 A176799
Adjacent sequences: A059051 A059052 A059053 * A059055 A059056 A059057
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KEYWORD
| nonn,changed
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Dec 21 2000
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