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

1,1

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

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 *)

Prog

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

Crossrefs

Cf. A007953, A055558.

Sequence in context: A256639 A058370 A230012 * A066007 A147830 A135162

Adjacent sequences: A164887 A164888 A164889 * A164891 A164892 A164893

Keyword

base,nonn

Author

Zak Seidov, Aug 29 2009

Extensions

Definition corrected by Michel Marcus, Oct 16 2013

Corrected by Robert Israel, May 02 2018

Status

approved