cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-15 of 15 results.

A196032 Numbers having at least one zero in base 4 representation.

Original entry on oeis.org

4, 8, 12, 16, 17, 18, 19, 20, 24, 28, 32, 33, 34, 35, 36, 40, 44, 48, 49, 50, 51, 52, 56, 60, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 88, 92, 96, 97, 98, 99, 100, 104, 108, 112, 113, 114, 115, 116, 120, 124, 128
Offset: 1

Views

Author

Reinhard Zumkeller, Oct 27 2011

Keywords

Links

Crossrefs

Cf. A023705 (complement).

Programs

  • Haskell
    a196032 n = a196032_list !! (n-1)
a196032_list = filter f [1..] where
   f 0 = False; f x = m == 0 || f x' where (x',m) = divMod x 4
-- Reinhard Zumkeller, Oct 19 2011
  • Mathematica
    Select[Range[200], DigitCount[#, 4, 0] > 0 &] (* Paolo Xausa, Mar 22 2025 *)

A023706 Numbers with a single 0 in their base 4 expansion.

Original entry on oeis.org

0, 4, 8, 12, 17, 18, 19, 20, 24, 28, 33, 34, 35, 36, 40, 44, 49, 50, 51, 52, 56, 60, 69, 70, 71, 73, 74, 75, 77, 78, 79, 81, 82, 83, 84, 88, 92, 97, 98, 99, 100, 104, 108, 113, 114, 115, 116, 120, 124, 133, 134, 135, 137, 138, 139, 141
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

Each member of the sequence is either 4*a+b for a in the sequence and b in {1,2,3}, or 4*a for a in A023705. - Robert Israel, Oct 04 2018

Links

Crossrefs

Cf. A023705.

Programs

  • Maple
    R23705:= {1,2,3}:
R:= {}: A:= 0;
for i from 1 to 4 do
  R:= map(t ->4*t, R23705) union map(t -> (4*t+1,4*t+2,4*t+3), R);
  R23705:= map(t -> (4*t+1,4*t+2,4*t+3), R23705);
  A:= A, op(sort(convert(R,list)));
od:
A; # Robert Israel, Oct 04 2018
  • Mathematica
    Select[ Range[ 0, 160 ], (Count[ IntegerDigits[ #, 4 ], 0 ]==1)& ]
  • PARI
    isok(n) = (n==0) || (#select(x->(x==0), digits(n, 4)) == 1); \\ Michel Marcus, Oct 04 2018

A382412 Numbers with no zeros in their base-7 representation.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90
Offset: 1

Views

Author

Paolo Xausa, Mar 24 2025

Keywords

Links

Crossrefs

Cf. zeroless numbers in other bases: A126646 (base 2), A032924 (base 3), A023705 (base 4), A023721 (base 5), A248910 (base 6), A255805 (base 8), A255808 (base 9), A052382 (base 10).
Cf. A007093, A043393, A249102, A382413 (complement).

Programs

  • Mathematica
    Select[Range[100], DigitCount[#, 7, 0] == 0 &]

A266001 Numbers with no 0's in their base 3 and base 4 expansions.

Original entry on oeis.org

1, 2, 5, 7, 13, 14, 22, 23, 25, 26, 41, 43, 53, 121, 122, 125, 149, 151, 157, 158, 214, 215, 229, 230, 233, 238, 239, 365, 367, 373, 374, 377, 445, 446, 473, 475, 485, 607, 617, 619, 634, 635, 637, 638, 697, 698, 701, 725, 727, 1366, 1367, 1373, 1375, 1429, 1430, 1445, 1447, 1453, 1454
Offset: 1

Views

Author

Robin Powell, Jan 27 2016

Keywords

Comments

Intersection of A023705 and A032924.
1, 7 and 32767 also share this property in base 2.

Examples

			53 is 1222 in base 3 and 311 in base 4; no zeros are shown in either representation and so 53 is a term.
Similarly, 121 is 11111 in base 3 and 1321 in base 4 so it is also a term.

Links

Crossrefs

Cf. A023705, A032924, A262958, A262963.

Programs

  • PARI
    isokd(n) = vecmin(digits(n, 3)) && vecmin(digits(n, 4)); \\ Michel Marcus, Jan 28 2016
  • Python
    from _future_ import division
from gmpy2 import digits
A266001_list = [j for j in (int(format(i,'b'),3)+(3**n-1)//2 for n in range(1,10) for i in range(2**n)) if '0' not in digits(j,4)] # Chai Wah Wu, Feb 13 2016

A259568 Numbers following gaps in the sequence of base-4 numbers that don't contain 0.

Original entry on oeis.org

1, 5, 9, 13, 21, 25, 29, 37, 41, 45, 53, 57, 61, 85, 89, 93, 101, 105, 109, 117, 121, 125, 149, 153, 157, 165, 169, 173, 181, 185, 189, 213, 217, 221, 229, 233, 237, 245, 249, 253, 341, 345, 349, 357, 361, 365, 373, 377, 381, 405, 409, 413, 421, 425, 429, 437, 441, 445, 469, 473, 477, 485, 489, 493, 501, 505, 509, 597, 601, 605
Offset: 1

Views

Author

Sean Oneil, Jun 30 2015

Keywords

Comments

Partial sums for the convergent modified harmonic series in base 4 excluding 0 = Sum of 1/a(n) + 1/(a(n) + 1) + 1/(a(n) + 2) = Sum of (3*a(n)^2 + 6*a(n) + 2)/(a(n)*(a(n) + 1)*(a(n) + 2)).

Examples

			Pattern of numbers of skipped terms (numbers in base 4 with at least one zero) is 1 (4 = 10_4), 1 (8 = 20_4), 1 (12 = 30_4), 4+1 (16 = 100_4, 17 = 101_4, 18 = 102_4, 19 = 103_4, 20 = 110_4), 1, 1, 4+1, 1, 1, 4+1, 1, 1, 16+4+1, ...

Links

Crossrefs

Subset of A016813 (congruent to 1 mod 4). a(n) = A023705(3n - 2). Each term is one more than the numbers that follow gaps in A196032.

Programs

  • PARI
    lista(nn)=prec0 = 1; for(n=1, nn, if (vecmin(digits(n, 4)), if (prec0, print1(n,, ", ")); prec0 = 0, prec0 = 1);); \\ Michel Marcus, Aug 03 2015
Previous Showing 11-15 of 15 results.

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