A075244 Least number requiring the base n to produce a prime by base reversal.

2, 3, 15, 8, 109, 9, 119, 16, 27, 70, 2197, 36, 1265, 158, 213, 178, 4205, 126, 14189, 260, 273, 304, 4865, 120, 1295, 78, 81, 532, 44323, 150, 47317, 952, 771, 102, 16705, 492, 6209, 114, 1209, 2020, 132743, 294, 22945, 2834, 2721, 2276, 66455, 144

Offset

1,1

Comments

Question, Is every base necessary to convert the natural numbers into primes?

Links

Table of n, a(n) for n=1..48.

Example

a(1) = 2 because two = 11 in unary (A000042) and its reversal 11 = 2. a(2) = 3 because three = 11 in base 2 (A007088) and its reversal 11 in base 2 = 3. a(3) = 15 because fifteen = 120 in base 3 (A007089) and its reversal 21 in base 3 = 7. a(4) = 8 -> 2. a(7) = 119 because 119 base 7 = 230 in base 7 (A007093) and its reversal 32 base 7 = 161.

Mathematica

f[n_] := Block[{b = 2}, While[b < n && !PrimeQ[ FromDigits[ Reverse[ IntegerDigits[n, b]], b]], b++ ]; If[b != n, b, 0]]; a = Table[0, {70}]; Do[b = f[n]; If[b < 76 && a[[b]] == 0, a[[b]] = n], {n, 2, 133000}]

Crossrefs

Cf. A075241 & A075242.

Sequence in context: A180698 A266618 A082572 * A342567 A088030 A101047

Adjacent sequences: A075241 A075242 A075243 * A075245 A075246 A075247

Keyword

base,easy,nonn

Author

Robert G. Wilson v, Sep 09 2002

Status

approved