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Search: id:A133522
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| A133522 |
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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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8
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| 5, 8, 12, 4, 2, 6, 20, 22, 8, 8, 12, 22, 26, 30, 20, 20, 74, 52, 22, 26, 4, 22, 6, 42, 40, 8, 58, 44, 42, 8, 40, 6, 36, 28, 2, 28, 6, 4, 20, 14, 2, 12, 8, 46, 2, 40, 10, 4, 110, 12, 18, 44, 42, 6, 24, 20, 8, 28, 46, 2, 18, 6, 60, 36, 24, 2, 18, 4, 24, 48, 6, 30, 6, 6, 22, 6, 2, 6, 2, 40, 2
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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p(2)=3, 3^5 = 243; 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: 243 + 2 = 245, which is 5 * 7^2 and not prime.
for k = 4: 243 + 4 = 247, which is 13 * 19, also not prime.
for k = 6: 243 + 6 = 249, which is 3 * 83, also not prime.
for k = 8: 243 + 8 = 251, which is prime, so 8 is the smallest number that can be added to 243 to make another prime.
Hence a(2) = 8.
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CROSSREFS
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Cf. A050997, A054271, A091666, A133517, A133518, A133519, A133520, A133521, (A001223).
Sequence in context: A006620 A056955 A023381 this_sequence A133269 A076635 A116602
Adjacent sequences: A133519 A133520 A133521 this_sequence A133523 A133524 A133525
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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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