|
%I #27 Sep 08 2022 08:44:51
%S 3,4,33,34,43,44,333,334,343,344,433,434,443,444,3333,3334,3343,3344,
%T 3433,3434,3443,3444,4333,4334,4343,4344,4433,4434,4443,4444,33333,
%U 33334,33343,33344,33433,33434,33443,33444,34333,34334
%N Numbers with digits 3 and 4 only.
%H Vincenzo Librandi, <a href="/A032834/b032834.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%F a(n) = A007931(n) + A002276(A000523(n+1)) = A032810(n) + A256077(n) etc. - _M. F. Hasler_, Mar 27 2015
%F From _Robert Israel_, Apr 03 2017:
%F a(2*n+1) = 10*a(n)+3.
%F a(2*n+2) = 10*a(n)+4.
%F G.f. g(x) satisfies g(x) = 10*(x+x^2)*g(x^2) + x*(3+4*x)/(1-x^2). (End)
%p S[1]:= [3,4]:
%p for d from 2 to 5 do S[d]:= map(t -> (10*t+3,10*t+4), S[d-1]) od:
%p seq(op(S[d]),d=1..5); # _Robert Israel_, Apr 03 2017
%t Flatten[Table[FromDigits[#,10]&/@Tuples[{3,4},n],{n,5}]] (* _Vincenzo Librandi_, May 30 2012 *)
%o (Magma) [n: n in [1..35000] | Set(IntegerToSequence(n, 10)) subset {3, 4}]; // _Vincenzo Librandi_, May 30 2012
%o (PARI) A032834(n)=vector(#n=binary(n+1)[2..-1],i,10^(#n-i))*n~+10^#n\3 \\ _M. F. Hasler_, Mar 27 2015
%Y Cf. A032829-A032833 (in other bases), A102659 (Lyndon words in this sequence), A007088 (digits 0 & 1), A007931 (digits 1 & 2), A032810 (digits 2 & 3), A256290 (digits 4 & 5), A256291 (digits 5 & 6), A256292 (digits 6 & 7), A256340 (digits 7 & 8), A256341 (digits 8 & 9).
%K nonn,base,easy
%O 1,1
%A _Clark Kimberling_
%E Crossrefs added by _M. F. Hasler_, Mar 27 2015
%E Name corrected by _Robert Israel_, Apr 03 2017
|
