A030373 Write n in base 4 and juxtapose.

1, 2, 3, 1, 0, 1, 1, 1, 2, 1, 3, 2, 0, 2, 1, 2, 2, 2, 3, 3, 0, 3, 1, 3, 2, 3, 3, 1, 0, 0, 1, 0, 1, 1, 0, 2, 1, 0, 3, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 2, 0, 1, 2, 1, 1, 2, 2, 1, 2, 3, 1, 3, 0, 1, 3, 1, 1, 3, 2, 1, 3, 3, 2, 0, 0, 2, 0, 1, 2, 0, 2, 2, 0, 3, 2, 1, 0

Offset

1,2

Comments

An irregular table in which the n-th row lists the base-4 digits of n. - Jason Kimberley, Nov 26 2012

The base-4 Champernowne constant: it is normal in base 4. - Jason Kimberley, Nov 26 2012

Links

R. J. Mathar, Table of n, a(n) for n = 1..4664

F. J. Aragon Artacho, D. H. Bailey, J. M. Borwein, and P. B. Borwein, Walking on real numbers, preprint September 2012.

Example

1;
2;
3;
1,0;
1,1;
1,2;
1,3;
2,0;
2,1;
2,2;
...
3,3;
1,0,0;
1,0,1;
1,0,2;
1,0,3;
1,1,0; ....

Mathematica

Flatten[IntegerDigits[Range[40], 4]] (* Harvey P. Dale, Aug 23 2011 *)

Prog

(Magma) &cat[Reverse(IntegerToSequence(n, 4)):n in[1..31]]; // Jason Kimberley, Dec 07 2012
(Python)
from itertools import count, chain, islice
from sympy.ntheory.factor_ import digits
def A030373_gen(): return chain.from_iterable(digits(m, 4)[1:] for m in count(1))
A030373_list = list(islice(A030373_gen(), 30)) # Chai Wah Wu, Jan 07 2022
(Python)
from sympy import digits
from oeis_sequences.OEISsequences import bisection, bsearch
def A030373(n):
    if n == 1: return 1
    def g(x): return x+(m:=x.bit_length()+1>>1)*(x+1)-((1<<(m-1<<1))-1<<2)//3
    def f(x): return n+1+bsearch(g, x)
    return int((s:=digits(a:=bisection(f, n+1, n+1)-n, 4))[n-1-a*(k:=len(s))+((1<<(k<<1))-1)//3]) # Chai Wah Wu, Mar 02 2026

Crossrefs

Cf. A007376, A003137, A007090.

Tables in which the n-th row lists the base b digits of n: A030190 and A030302 (b=2), A003137 and A054635 (b=3), this sequence (b=4), A031219 (b=5), A030548 (b=6), A030998 (b=7), A031035 and A054634 (b=8), A031076 (b=9), A007376 and A033307 (b=10). - Jason Kimberley, Dec 06 2012

Sequence in context: A353493 A321932 A321933 * A079343 A004566 A321896

Adjacent sequences: A030370 A030371 A030372 * A030374 A030375 A030376

Keyword

nonn,base,cons,tabf,easy

Author

Clark Kimberling

Status

approved