A247182 Numbers k such that the smallest k-digit odd number concatenated with the largest k-digit odd number is prime.

1, 3, 9, 21, 5571, 6493, 14481

Offset

1,2

Comments

Numbers k such that 10^(k-1)+1 concatenated with 10^k-1 is prime.

a(7) > 10^4.

From Robert Israel, Jan 08 2017: (Start)

Numbers k such that 10^(2k-1) + 2*10^k - 1 is prime.

All terms are odd. (End)

a(8) > 24292. - J.W.L. (Jan) Eerland, Apr 08 2023

Links

Table of n, a(n) for n=1..7.

Example

The smallest and largest odd 3-digit numbers are 101 and 999, respectively. Since 101999 is prime, 3 is a term of the sequence.
The smallest and largest odd 4-digit numbers are 1001 and 9999, respectively. Since 10019999 is not prime, 4 is not a term of this sequence.

Maple

select(n -> isprime(10^(2*n-1)+2*10^n-1), [seq(i, i=1..1000, 2)]); # Robert Israel, Jan 08 2017

Mathematica

k=1; Monitor[Parallelize[While[True, If[FromDigits[Join@@IntegerDigits/@{10^(k-1)+1, 10^k-1}]//PrimeQ, Print[k]]; k++]; k], k] (* J.W.L. (Jan) Eerland, Apr 08 2023 *)

Prog

(PARI) f(n)=eval(concat(Str(10^(n-1)+1), 10^n-1))
for(n=1, 10^4, if(ispseudoprime(f(n)), print1(n, ", ")))

Crossrefs

Cf. A247183.

Sequence in context: A362341 A098980 A007647 * A363967 A318807 A063586

Adjacent sequences: A247179 A247180 A247181 * A247183 A247184 A247185

Keyword

nonn,hard,more,base

Author

Derek Orr, Nov 22 2014

Extensions

a(7) from J.W.L. (Jan) Eerland, Apr 08 2023

Status

approved