A160383 -id:A160383 - cp's OEIS frontend

A292373 A binary encoding of 3-digits in base-4 representation of n.

0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 2, 2, 3, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 2, 2, 3, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 2, 2, 3, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 5, 6, 6, 6, 7, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 2, 2, 3, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 2, 2, 3, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 2, 2, 3, 4, 4, 4, 5, 4, 4, 4, 5, 4

Offset: 0

Antti Karttunen, Sep 15 2017

			   n      a(n)     base-4(n)  binary(a(n))
                  A007090(n)  A007088(a(n))
  --      ----    ----------  ------------
   1        0          1           0
   2        0          2           0
   3        1          3           1
   4        0         10           0
   5        0         11           0
   6        0         12           0
   7        1         13           1
   8        0         20           0
   9        0         21           0
  10        0         22           0
  11        1         23           1
  12        2         30          10
  13        2         31          10
  14        2         32          10
  15        3         33          11
  16        0        100           0
  17        0        101           0
  18        0        102           0
  19        1        103           1

Antti Karttunen, Table of n, a(n) for n = 0..65536
Index entries for sequences related to binary expansion of n

Cf. A007088, A007090, A048735, A059905, A059906, A160383, A213370, A292370, A292371, A292372.

def A292373(n): return int(bin(n&n>>1)[:1:-2][::-1],2) # Chai Wah Wu, Jun 30 2022

a(n) = A059905(A048735(n)) = A059906(A213370(n)).

For all n >= 0, A000120(a(n)) = A160383(n).

A039005 Numbers whose base-4 representation has the same number of 1's and 3's.

Original entry on oeis.org

0, 2, 7, 8, 10, 13, 19, 27, 28, 30, 32, 34, 39, 40, 42, 45, 49, 52, 54, 57, 67, 75, 76, 78, 95, 99, 107, 108, 110, 112, 114, 119, 120, 122, 125, 128, 130, 135, 136, 138, 141, 147, 155, 156, 158, 160, 162, 167, 168, 170, 173, 177, 180, 182, 185, 193, 196, 198

Offset: 1

Olivier Gérard

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A007090, A160381, A160383.

Cf. A004171 (subsequence).

A031466 Numbers whose base-4 representation has one fewer 0 than 3's.

Original entry on oeis.org

3, 7, 11, 13, 14, 23, 27, 29, 30, 39, 43, 45, 46, 51, 53, 54, 57, 58, 60, 79, 87, 91, 93, 94, 103, 107, 109, 110, 115, 117, 118, 121, 122, 124, 143, 151, 155, 157, 158, 167, 171, 173, 174, 179, 181, 182, 185, 186, 188, 199, 203, 205

Offset: 1

Clark Kimberling

Numbers n such that A160383(n) - A160380(n) = 1. - Robert Israel, Jun 05 2018

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A007090, A160380, A160383.

filter:= proc(n) local L;
  L:= convert(n,base,4);
  numboccur(3,L) - numboccur(0,L)=1
end proc:
select(filter, [$1..300]); # Robert Israel, Jun 05 2018

Select[Range[210],DigitCount[#,4,0]==DigitCount[#,4,3]-1&] (* Harvey P. Dale, Dec 16 2011 *)

A039006 Numbers whose base-4 representation has the same number of 2's and 3's.

Original entry on oeis.org

0, 1, 4, 5, 11, 14, 16, 17, 20, 21, 27, 30, 35, 39, 44, 45, 50, 54, 56, 57, 64, 65, 68, 69, 75, 78, 80, 81, 84, 85, 91, 94, 99, 103, 108, 109, 114, 118, 120, 121, 131, 135, 140, 141, 147, 151, 156, 157, 175, 176, 177, 180, 181, 187, 190, 194, 198, 200, 201, 210

Offset: 1

Olivier Gérard

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A007090, A160382, A160383, A039005.

Cf. A000302, A052539 (subsequences).

Select[Range[0,250],DigitCount[#,4,2]==DigitCount[#,4,3]&] (* Harvey P. Dale, Mar 19 2017 *)

A338854 Product of the nonzero digits of (n written in base 4).

Original entry on oeis.org

1, 1, 2, 3, 1, 1, 2, 3, 2, 2, 4, 6, 3, 3, 6, 9, 1, 1, 2, 3, 1, 1, 2, 3, 2, 2, 4, 6, 3, 3, 6, 9, 2, 2, 4, 6, 2, 2, 4, 6, 4, 4, 8, 12, 6, 6, 12, 18, 3, 3, 6, 9, 3, 3, 6, 9, 6, 6, 12, 18, 9, 9, 18, 27, 1, 1, 2, 3, 1, 1, 2, 3, 2, 2, 4, 6, 3, 3, 6, 9, 1

Offset: 0

Ilya Gutkovskiy, Nov 12 2020

Cf. A007090, A051801, A117592, A160382, A160383, A309954.

Table[Times @@ DeleteCases[IntegerDigits[n, 4], 0], {n, 0, 80}]
nmax = 80; A[] = 1; Do[A[x] = (1 + x + 2 x^2 + 3 x^3) A[x^4] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

a(n) = vecprod(select(x->x, digits(n, 4))); \\ Michel Marcus, Nov 12 2020

G.f. A(x) satisfies: A(x) = (1 + x + 2*x^2 + 3*x^3) * A(x^4).

a(n) = 2^A160382(n) * 3^A160383(n).

cp's OEIS Frontend

A292373 A binary encoding of 3-digits in base-4 representation of n.

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A039005 Numbers whose base-4 representation has the same number of 1's and 3's.

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A031466 Numbers whose base-4 representation has one fewer 0 than 3's.

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A039006 Numbers whose base-4 representation has the same number of 2's and 3's.

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A338854 Product of the nonzero digits of (n written in base 4).

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