A032834 Numbers with digits 3 and 4 only.

3, 4, 33, 34, 43, 44, 333, 334, 343, 344, 433, 434, 443, 444, 3333, 3334, 3343, 3344, 3433, 3434, 3443, 3444, 4333, 4334, 4343, 4344, 4433, 4434, 4443, 4444, 33333, 33334, 33343, 33344, 33433, 33434, 33443, 33444, 34333, 34334

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for 10-automatic sequences.

Formula

a(n) = A007931(n) + A002276(A000523(n+1)) = A032810(n) + A256077(n) etc. - M. F. Hasler, Mar 27 2015

From Robert Israel, Apr 03 2017:

a(2*n+1) = 10*a(n)+3.

a(2*n+2) = 10*a(n)+4.

G.f. g(x) satisfies g(x) = 10*(x+x^2)*g(x^2) + x*(3+4*x)/(1-x^2). (End)

Maple

S[1]:= [3, 4]:
for d from 2 to 5 do S[d]:= map(t -> (10*t+3, 10*t+4), S[d-1]) od:
seq(op(S[d]), d=1..5); # Robert Israel, Apr 03 2017

Mathematica

Flatten[Table[FromDigits[#, 10]&/@Tuples[{3, 4}, n], {n, 5}]] (* Vincenzo Librandi, May 30 2012 *)

Prog

(Magma) [n: n in [1..35000] | Set(IntegerToSequence(n, 10)) subset {3, 4}]; // Vincenzo Librandi, May 30 2012
(PARI) A032834(n)=vector(#n=binary(n+1)[2..-1], i, 10^(#n-i))*n~+10^#n\3 \\ M. F. Hasler, Mar 27 2015

Crossrefs

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).

Sequence in context: A042431 A269724 A296250 * A025140 A246015 A078504

Adjacent sequences: A032831 A032832 A032833 * A032835 A032836 A032837

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

Crossrefs added by M. F. Hasler, Mar 27 2015

Name corrected by Robert Israel, Apr 03 2017

Status

approved