cp's OEIS Frontend

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

%I A164890 #16 May 08 2018 08:00:28
%S A164890 19,199,919,991,1999,9199,99991,199999,991999,999199,9999991,19999999,
%T A164890 99991999,9199999999,11111111911,11119111111,99999199999,99999991999,
%U A164890 111111911191,111191119111,111911191111,191119111111,991999999999,999999991999,1111111119919,1111111191199,1111111191919,1111111199119
%N A164890 Primes composed of digit {1,9} and with digit sum 9*k+1.
%C A164890 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
%C A164890 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
%H A164890 Robert Israel, <a href="/A164890/b164890.txt">Table of n, a(n) for n = 1..10000</a>
%p A164890 Res:= {}:
%p A164890 for d from 2 to 14 do
%p A164890   for j from 1 to d by 9 do
%p A164890     Res:= Res union select(isprime, {seq((10^d-1)/9 + 8*add(10^i,i=s), s = combinat:-choose([$0..d-1],d-j))})
%p A164890 od od:
%p A164890 sort(convert(Res,list)); # _Robert Israel_, May 02 2018
%t A164890 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 *)
%o A164890 (PARI) isok(n) = isprime(n) && (Set(digits(n)) == [1, 9]) && ((sumdigits(n) % 9) == 1); \\ _Michel Marcus_, Oct 16 2013
%Y A164890 Cf. A007953, A055558.
%K A164890 base,nonn
%O A164890 1,1
%A A164890 _Zak Seidov_, Aug 29 2009
%E A164890 Definition corrected by _Michel Marcus_, Oct 16 2013
%E A164890 Corrected by _Robert Israel_, May 02 2018