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Search: id:A133521
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| A133521 |
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Smallest k such that p(n)^5 - k is prime where p(n) is the n-th prime. |
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+0
8
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| 1, 2, 4, 20, 4, 2, 18, 18, 16, 6, 2, 6, 24, 12, 36, 22, 10, 8, 8, 24, 20, 86, 22, 6, 18, 42, 26, 6, 50, 52, 20, 12, 48, 2, 196, 68, 18, 14, 16, 16, 18, 2, 10, 6, 16, 38, 2, 36, 6, 2, 16, 42, 18, 42, 40, 34, 22, 2, 38, 4, 36, 52, 26, 132, 36, 28, 24, 74, 46, 36, 4, 16, 8, 24, 80, 16
(list; graph; listen)
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OFFSET
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1,2
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EXAMPLE
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p(10)=29, 29^5 = 20511149; for odd k, and n > 1, p(n)^r - k is even and thus not prime, so we only need consider even k.
for k = 2: 20511149 - 2 = 20511147, which is 3 * 23 * 297263 and not prime.
for k = 4: 20511149 - 4 = 20511145, which is 5 * 4102229, also not prime.
for k = 6: 20511149 - 6 = 20511141, which is prime, so 6 is the smallest number that can be subtracted from 20511149 to make another prime.
Hence a(10) = 6.
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CROSSREFS
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Cf. A050997, A054271, A091666, A133517, A133518, A133519, A133520, A133522, (A001223).
Adjacent sequences: A133518 A133519 A133520 this_sequence A133522 A133523 A133524
Sequence in context: A061213 A063458 A132530 this_sequence A122158 A033180 A069535
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KEYWORD
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easy,nonn
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AUTHOR
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Carl R. White (oeisfan(AT)phodd.net), Sep 14 2007
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