A164890 Primes composed of digit {1,9} and with digit sum 9*k+1.

19, 199, 919, 991, 1999, 9199, 99991, 199999, 991999, 999199, 9999991, 19999999, 99991999, 9199999999, 11111111911, 11119111111, 99999199999, 99999991999, 111111911191, 111191119111, 111911191111, 191119111111, 991999999999, 999999991999, 1111111119919, 1111111191199, 1111111191919, 1111111199119

Offset: 1

Author

Zak Seidov, Aug 29 2009

Keywords

• base
• nonn

Comments

Corresponding k's are 1, 2, 2, 2, 3, 3, 4, 5, 5, 5, 6, 7, 7, 9, 2, 2, 10, 10, 3, 3, 3, 3, 11, 11, 4, 4, 4, 4. - Robert Israel, May 02 2018

Number of primes having a digital length of k=1,2,3...: 0, 1, 3, 2, 1, 3, 1, 2, 0, 1, 4, 6, 33, 81, 329, 455, 2028, 3134, 9193, 9060, 31615, 39246, 88069, 94794, 252965, 309437, ..., . = Robert G. Wilson v, May 05 2018

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007953, A055558.

Programs

Maple

Res:= {}:
for d from 2 to 14 do
  for j from 1 to d by 9 do
    Res:= Res union select(isprime, {seq((10^d-1)/9 + 8*add(10^i,i=s), s = combinat:-choose([$0..d-1],d-j))})
od od:
sort(convert(Res,list)); # Robert Israel, May 02 2018

Mathematica

f[n_] := Block[{s, t = Tuples[{1, 9}, n]}, s = Select[t, Mod[Plus @@ #, 9] == 1 &]; Select[ FromDigits@# & /@ s, PrimeQ]]; Array[f, 12] // Flatten (* Robert G. Wilson v, May 04 2018 *)

PARI

isok(n) = isprime(n) && (Set(digits(n)) == [1, 9]) && ((sumdigits(n) % 9) == 1); \\ Michel Marcus, Oct 16 2013

Extensions

Definition corrected by Michel Marcus, Oct 16 2013

Corrected by Robert Israel, May 02 2018