A130217 Smallest prime with number of digits equal to n-th Lucas number A000032(n).

11, 2, 101, 1009, 1000003, 10000000019, 100000000000000003, 10000000000000000000000000331, 10000000000000000000000000000000000000000000121, 1000000000000000000000000000000000000000000000000000000000000000000000000129

Offset

0,1

Comments

This is to Lucas numbers as A130150 is to Fibonacci numbers.

Links

Table of n, a(n) for n=0..9.

Formula

a(n) = A003617(A000032(n)) = (MIN{p(i) such that p(i) is prime and number of digits of decimal expansion of p(i) = L(n) for Lucas number L(n)} = MIN{A000040(i) such that A055642(A000040(i)) = A000032(n)}.

Example

a(0) = 11 because L(0) = A000032(0) = 2 and 11 is the smallest 2 digit prime.
a(1) = 2 because L(1) = A000032(1) = 1 and 2 is the smallest 1 digit prime.
a(2) = 101 because L(2) = A000032(2) = 3 and 101 is the smallest 3 digit prime.

Mathematica

NextPrime/@(10^(LucasL[Range[0, 10]]-1)) (* Harvey P. Dale, Aug 28 2013 *)

Crossrefs

Cf. A000032, A000040, A003617, A130150.

Sequence in context: A095157 A110767 A089365 * A096044 A160464 A038316

Adjacent sequences: A130214 A130215 A130216 * A130218 A130219 A130220

Keyword

easy,nonn,base,less

Author

Jonathan Vos Post, Aug 04 2007

Extensions

One more term (a(9)) from Harvey P. Dale, Aug 28 2013

Status

approved