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%I #11 May 23 2021 02:51:06
%S 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,
%T 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,
%U 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
%N Least base for which the n-th composite number whose reversal in that base is a prime, or zero if impossible.
%C 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.
%H Amiram Eldar, <a href="/A075242/b075242.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t 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}]
%Y Cf. A075241, A075241.
%K base,easy,nonn
%O 1,2
%A _Robert G. Wilson v_, Sep 09 2002
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