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 A075242 Least base for which the n-th composite number whose reversal in that base is a prime, or zero if impossible. 5
 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; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Question: Other than 4, is there a composite that cannot be made a prime by base reversal? I have found none < (10^5)-th composite. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE 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. MATHEMATICA 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}] CROSSREFS Cf. A075241, A075241. Sequence in context: A004517 A254350 A056649 * A161489 A050975 A053446 Adjacent sequences:  A075239 A075240 A075241 * A075243 A075244 A075245 KEYWORD base,easy,nonn AUTHOR Robert G. Wilson v, Sep 09 2002 STATUS approved

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Last modified September 20 03:47 EDT 2021. Contains 347577 sequences. (Running on oeis4.)