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A109291
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New factors appearing in the factorization of 5^k - 2^k as k increases.
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0
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3, 7, 13, 29, 1031, 19, 25999, 641, 5563, 11, 41, 1409, 11551, 541, 406898311, 1597, 31, 8161, 17, 22993, 82009, 3101039, 37, 397, 6357828601279, 61, 5521
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Zsigmondy numbers for a = 5, b = 2: Zs(n, 5, 2) is the greatest divisor of 5^k - 2^k that is relatively prime to 5^j - 2^j for all positive integers j < k. We show only through k = 20, ready for extension and Mathematica.
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LINKS
| MathWorld, Zsigmondy's Theorem
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EXAMPLE
| a(1) = 3 because 5^1 - 2^1 = 3.
a(2) = 7 because, although 5^2 - 2^2 = 21 = 3 * 7 has prime factor 3, that has already appeared in this sequence, but the factor of 7 is new.
a(3) = 13 because, although 5^3 - 2^3 = 117 = 3^2 * 13 has repeated prime factor 3, that has already appeared in this sequence, but the prime factor of 13 is new.
a(4) = 29 because, although 5^4 - 2^4 = 2385 = 609 = 3 * 7 * 29, the prime factors of 3 and 7 have already appeared in this sequence, but the prime factor of 29 is new.
a(5) = 1031 because, although 5^5 - 2^5 = 16775 = 3093 = 3 * 1031, the prime factor of 3 has already appeared in this sequence, but the prime factors of 1031 is new.
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CROSSREFS
| Cf. A109325, A109347, A109348, A109349, my submission of 10 minutes ago Zs(n, 7, 2).
Sequence in context: A091565 A025249 A147098 * A199218 A062700 A136060
Adjacent sequences: A109288 A109289 A109290 * A109292 A109293 A109294
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 25 2005
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EXTENSIONS
| Comment corrected by Jerry Metzger, Nov 04 2009
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