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Search: id:A133519
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| A133519 |
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Smallest k such that p(n)^4 - k is prime where p(n) is the n-th prime. |
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8
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| 3, 2, 6, 2, 2, 2, 24, 14, 18, 2, 8, 8, 2, 2, 12, 2, 2, 24, 24, 38, 2, 8, 2, 54, 12, 2, 12, 12, 44, 18, 14, 18, 12, 32, 12, 24, 38, 14, 12, 12, 54, 2, 50, 8, 32, 8, 12, 14, 24, 8, 8, 2, 2, 12, 18, 30, 50, 12, 2, 24, 12, 2, 32, 2, 84, 12, 8, 12, 8, 74, 14, 18, 2, 20, 24, 14, 2, 14, 14, 2, 18
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OFFSET
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1,1
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EXAMPLE
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p(3)=5, 5^4 = 625; 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: 625 - 2 = 623, which is 7 * 89 and not prime.
for k = 4: 625 - 4 = 621, which is 3^3 * 23, also not prime.
for k = 6: 625 - 6 = 619, which is prime, so 6 is the smallest number that can be subtracted from 625 to make another prime.
Hence a(3) = 6.
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CROSSREFS
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Cf. A030814, A054271, A091666, A133517, A133518, A133520, A133521, A133522, (A001223).
Sequence in context: A016460 A097887 A019761 this_sequence A135223 A131897 A061187
Adjacent sequences: A133516 A133517 A133518 this_sequence A133520 A133521 A133522
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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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