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%I #16 Jan 30 2017 17:27:32
%S 109,1009,10009,10099,100999,1000099,1000999,1000000009,1000009999,
%T 1000099999,1009999999,10000000999,10000099999,10999999999,
%U 100999999999,1000000009999,1000000999999,1099999999999,10000000000099,10009999999999
%N Primes of the form m = 10^i + 10^j - 1, where i > j >= 0.
%C Numbers with the first digit 1 followed by at least one 0-digit and ending with a number > 0 of trailing 9-digits.
%C The digital sum of a term 10^i + 10^j - 1 is = 1 + 9*j == 1 (mod 9).
%C 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.
%H Harvey P. Dale, <a href="/A239720/b239720.txt">Table of n, a(n) for n = 1..1000</a> (* First 44 terms from Hieronymus Fischer *)
%e a(1) = 109, since 109 = 10^2 + 10^1 - 1 is prime.
%e a(2) = 1009, since 1009 = 10^3 + 10^1 - 1 is prime.
%t Select[Flatten[Table[10^i+10^j-1,{i,0,20},{j,0,i-1}]],PrimeQ] (* _Harvey P. Dale_, Jan 30 2017 *)
%o (Smalltalk)
%o A239720
%o "Answer the n-th term of A239720.
%o Usage: n A239720
%o Answer: a(n)"
%o | a b i j k p q terms |
%o terms := OrderedCollection new.
%o k := 0.
%o b := 10.
%o p := b.
%o i := 1.
%o [k < self] whileTrue:
%o [j := 0.
%o q := 1.
%o [j < i and: [k < self]] whileTrue:
%o [a := p + q - 1.
%o a isPrime
%o ifTrue:
%o [k := k + 1.
%o terms add: a].
%o q := b * q.
%o j := j + 1].
%o i := i + 1.
%o p := b * p].
%o ^terms at: self
%o --------------------
%o (Smalltalk)
%o A239720
%o "Version2: Answer an array of the first n terms of A239720.
%o Uses method primesWhichAreDistinctPowersOf: b withOffset: d from A239712.
%o Usage: n A239720
%o Answer: #(109 1009 ... ) [a(1) ... a(n)]"
%o ^self primesWhichAreDistinctPowersOf: 10 withOffset: -1
%K nonn
%O 1,1
%A _Hieronymus Fischer_, Apr 14 2014
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