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Search: id:A075242
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| A075242 |
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Least base for which the n-th composite number whose reversal in that base is a prime, or zero if impossible. |
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+0
3
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| 0, 2, 4, 6, 2, 2, 2, 3, 8, 3, 2, 3, 2, 2, 2, 2, 9, 2, 6, 4, 3, 2, 3, 12, 6, 3, 2, 6, 2, 3, 2, 2, 3, 2, 9, 2, 3, 2, 2, 3, 2, 12, 2, 3, 12, 3, 6, 2, 3, 10, 6, 2, 3, 10, 2, 26, 2, 27, 2, 12, 3, 2, 9, 2, 12, 2, 2, 3, 2, 3, 2, 4, 3, 2, 34, 2, 3, 2, 6, 2, 3, 2, 38, 2, 2, 3, 4, 7, 24, 2, 2, 3, 2, 3, 18, 4, 18
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Question, other than 4, is there a composite which can not be made a prime by base reversal? I have found none < 10^5-th composite.
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EXAMPLE
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a(1) = 0 because 4 (2) = 1 and 4 (3) = 4 and any base greater than 3 always gives the composite 4 as its base reversal. a(3) = 4 because 8 (2) = 1, 8 (3) = 8 but 8 (4) = 2 a prime.
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MATHEMATICA
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Composite[n_] := FixedPoint[n + PrimePi[ # ] + 1 &, n]; f[n_] := Block[{b = 2}, While[b < n && !PrimeQ[ FromDigits[ Reverse[ IntegerDigits[n, b]], b]], b++ ]; If[b != n, b, 0]]; Table[ f[ Composite[n]], {n, 1, 105}]
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CROSSREFS
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Adjacent sequences: A075239 A075240 A075241 this_sequence A075243 A075244 A075245
Sequence in context: A080413 A004517 A056649 this_sequence A050975 A053446 A133903
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KEYWORD
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base,easy,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 09 2002
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