A124244 a(n) is the smallest odd prime p such that 2^n*p has n digits but has at most two distinct digits; or 0 if no such prime exists.

3, 3, 29, 101, 691, 15467, 39023, 71023, 437977, 4344227, 21158903, 109739989, 344590189, 2956838897, 6781690193, 0, 85533990571, 3390460543777, 0, 53936545044581, 0, 0, 5298071316879193, 0, 168548719780643483

Offset

1,1

Comments

Andrew Rupinski showed that a(95) exists (see the links below).

Links

Table of n, a(n) for n=1..25.

Prime Puzzles & Problems Connection, Puzzle 376. n=p*2^x.

Andrew Rupinski, Prime Curios!.

Example

a(14)=2956838897 because 2^14*2956838897=48444848488448 has 14 digits with two distinct digits and 2956838897 is the smallest prime p such that 2^14*p has these properties.

Mathematica

a[1]=3; a[n_]:=(For[m=Floor[5^(n-1)/2], !(PrimeQ[m]&&Length[Union[ IntegerDigits[2^n*m]]]==2&&Length[IntegerDigits[2^n*m]]==n), m++ ]; m); Do[Print[a[n]], {n, 14}]

Crossrefs

Cf. A124245.

Sequence in context: A138962 A139206 A100651 * A351990 A151480 A096351

Adjacent sequences: A124241 A124242 A124243 * A124245 A124246 A124247

Keyword

nonn,base

Author

Farideh Firoozbakht, Oct 25 2006

Extensions

Edited by Don Reble, Oct 29 2006

Status

approved