A239720 Primes of the form m = 10^i + 10^j - 1, where i > j >= 0.

109, 1009, 10009, 10099, 100999, 1000099, 1000999, 1000000009, 1000009999, 1000099999, 1009999999, 10000000999, 10000099999, 10999999999, 100999999999, 1000000009999, 1000000999999, 1099999999999, 10000000000099, 10009999999999

Offset: 1

Author

Hieronymus Fischer, Apr 14 2014

Keywords

• nonn

Comments

Numbers with the first digit 1 followed by at least one 0-digit and ending with a number > 0 of trailing 9-digits.

The digital sum of a term 10^i + 10^j - 1 is = 1 + 9*j == 1 (mod 9).

Numbers m that satisfy m = 10^i + 10^j + 1 are never primes, since the digital sum of m is 3, and thus, m is divisible by 3.

Examples

			a(1) = 109, since 109 = 10^2 + 10^1 - 1 is prime.
a(2) = 1009, since 1009 = 10^3 + 10^1 - 1 is prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000 (First 44 terms from Hieronymus Fischer)

Programs

Mathematica

Select[Flatten[Table[10^i+10^j-1,{i,0,20},{j,0,i-1}]],PrimeQ] (* Harvey P. Dale, Jan 30 2017 *)

Smalltalk

A239720
  "Answer the n-th term of A239720.
  Usage: n A239720
  Answer: a(n)"
  | a b i j k p q terms |
  terms := OrderedCollection new.
  k := 0.
  b := 10.
  p := b.
  i := 1.
  [k < self] whileTrue:
         [j := 0.
         q := 1.
         [j < i and: [k < self]] whileTrue:
                   [a := p + q - 1.
                   a isPrime
                        ifTrue:
                            [k := k + 1.
                            terms add: a].
                   q := b * q.
                   j := j + 1].
         i := i + 1.
         p := b * p].
  ^terms at: self
--------------------

Smalltalk

A239720
  "Version2: Answer an array of the first n terms of A239720.
  Uses method primesWhichAreDistinctPowersOf: b withOffset: d from A239712.
  Usage: n A239720
  Answer: #(109 1009 ... ) [a(1) ... a(n)]"
  ^self primesWhichAreDistinctPowersOf: 10 withOffset: -1