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A059055
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Primes which can be written as (b^k+1)/(b+1) for positive integers b and k.
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4
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3, 7, 11, 13, 31, 43, 61, 73, 157, 211, 241, 307, 421, 463, 521, 547, 601, 683, 757, 1123, 1483, 1723, 2551, 2731, 2971, 3307, 3541, 3907, 4423, 4831, 5113, 5701, 6007, 6163, 6481
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| For (b^k+1)/(b+1) to be a prime, k must be an odd prime. 2=(0^0+1)/(0+1) has been excluded since neither b nor k would be positive.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..3880
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 = 89; maxdata = (1 + max^3)/(1 + max); a = {}; Do[i = 1; While[i = i + 2; cc = (1 + m^i)/(1 + m); cc <= maxdata, If[PrimeQ[cc], a = Append[a, cc]]], {m, 2, max}]; Sort[DeleteDuplicates[a]] (* Lei Zhou, Feb 08 2012 *)
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CROSSREFS
| Cf. A002383, A059054.
Cf. A003424, A085104.
Sequence in context: A154832 A164568 A053728 * A145670 A004061 A000572
Adjacent sequences: A059052 A059053 A059054 * A059056 A059057 A059058
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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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