A075242 Least base for which the n-th composite number whose reversal in that base is a prime, or zero if impossible.

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

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: A357049 A364864 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