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Search: id:A067022
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| A067022 |
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Exponent of largest power of (n+1)-st prime which is still smaller than the product of first n primes, the n-th primorial. |
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+0
2
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| 0, 1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 11, 11, 12, 13, 14, 15, 15, 16, 17, 18, 19, 19, 20, 21, 22, 22, 23, 24, 25, 26, 27, 27, 28, 29, 30, 31, 31, 32, 33, 34, 35, 35, 36, 37, 38, 39, 40, 41, 41, 42, 43, 44, 45, 46, 47, 47, 48, 49, 50, 51, 51, 52, 53, 54, 55, 55, 56, 57, 58
(list; graph; listen)
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OFFSET
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1,4
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FORMULA
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a(n)=Max{k; p(n+1)^k < A002110(n)} a(n)< n is trivial
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EXAMPLE
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1 < 2 < 2, 5^1 < 6 = 2.3 < 5^2, 11 < 2.3.5 < 121, 169 < 210 < 2197, 13^3 = 2197 < 2.3.5.7.11 < 28561, provide first 5 terms:0, 1, 1, 2, 3 17^3 = 4913 < q(6) = 30030 < 17^4 = 83521 gives a(6) = 3 19^4 = 130321 < q(7) = 510510 < 19^5 = 2476099 gives a(7) = 4
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MATHEMATICA
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q[x_] := Apply[Times, Table[Prime[w], {w, 1, x}]] Table[Count[Sign[Table[Prime[w+1]^k-q[w], {k, 1, w}]], -1], {w, 1, 100}]
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CROSSREFS
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Cf. A002110, A067021.
Sequence in context: A131737 A066481 A121928 this_sequence A113818 A136746 A003003
Adjacent sequences: A067019 A067020 A067021 this_sequence A067023 A067024 A067025
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Dec 29 2001
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