A039215 -id:A039215 - cp's OEIS frontend

A248910 Numbers with no zeros in base-6 representation.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92

Offset: 1

Reinhard Zumkeller, Mar 08 2015

Different from A039215, A047253, A184522, A187390, A194386.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Wikipedia, Senary
Index entries for 6-automatic sequences.

Cf. A007092, A100969 (subsequence).

Zeroless numbers in some other bases <= 10: A000042 (base 2), A032924 (base 3), A023705 (base 4), A255805 (base 8), A255808 (base 9), A052382 (base 10).

a248910 n = a248910_list !! (n-1)
a248910_list = iterate f 1 where
   f x = 1 + if r < 5 then x else 6 * f x'  where (x', r) = divMod x 6

Select[Range[100], DigitCount[#,6, 0] == 0 &] (* Paolo Xausa, Jun 29 2025 *)

isok(m) = vecmin(digits(m, 6)) > 0; \\ Michel Marcus, Jan 23 2022

from sympy import integer_log
def A248910(n):
    m = integer_log(k:=(n<<2)+1,5)[0]
    return sum((1+(k-5**m)//(5**j<<2)%5)*6**j for j in range(m)) # Chai Wah Wu, Jun 28 2025

A108120 Floor[n*1/Sin[1]], or Beatty sequence for 1/sin(1).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 83, 84, 85

Offset: 1

Zak Seidov, Jun 04 2005

nonn

Complement of A108587; not the same as A108586: a(37)=43 <> A108586(37)=44. - Reinhard Zumkeller, Jun 11 2005

Cf. A023800, A031943, A037918, A039215, A043091, A047253.

Cf. A108593.

a[n_]:=Floor[n*1/Sin[1]];Table[a[n], {n, 90}]

a(n) = floor(n*1/sin(1))

A108611 Excess of Beatty-function of 1/sin(1) over n.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16

Offset: 0

Zak Seidov, Jun 13 2005

nonn

Cf. A023800, A031943, A037918, A039215, A043091, A047253, A108120.

a(n) = A108120[n] - n.

A108612 Beatty-2 (or nested Beatty) sequence for 1/sin(1).

Original entry on oeis.org

1, 4, 9, 16, 25, 42, 56, 72, 90, 110, 143, 168, 195, 224, 255, 304, 340, 378, 418, 460, 504, 572, 621, 672, 725, 780, 864, 924, 986, 1050, 1116, 1216, 1287, 1360, 1435, 1512, 1591, 1710, 1794, 1880, 1968, 2058, 2193, 2288, 2385, 2484, 2585, 2736, 2842, 2950

Offset: 1

Zak Seidov, Jun 13 2005

nonn

Cf. A023800, A031943, A037918, A039215, A043091, A047253, A108120, A108611, A108613.

a(n) = floor(n*floor(n/sin(1))).

A108613 Excess of Beatty-2 function of 1/sin(1) over n^2.

Original entry on oeis.org

0, 0, 0, 0, 0, 6, 7, 8, 9, 10, 22, 24, 26, 28, 30, 48, 51, 54, 57, 60, 63, 88, 92, 96, 100, 104, 135, 140, 145, 150, 155, 192, 198, 204, 210, 216, 222, 266, 273, 280, 287, 294, 344, 352, 360, 368, 376, 432, 441, 450, 459, 468, 477, 540, 550, 560, 570, 580, 649, 660

Offset: 0

Zak Seidov, Jun 13 2005

nonn

Cf. A108612 Beatty-2 (or nested Beatty) function of 1/sin(1).

Cf. A023800, A031943, A037918, A039215, A043091, A047253, A108120, A108611, A108612.

a(n) = A108612[n] - n^2 = floor(n*floor(n/sin(1))) - n^2.

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A248910 Numbers with no zeros in base-6 representation.

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A108120 Floor[n*1/Sin[1]], or Beatty sequence for 1/sin(1).

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A108611 Excess of Beatty-function of 1/sin(1) over n.

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A108612 Beatty-2 (or nested Beatty) sequence for 1/sin(1).

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A108613 Excess of Beatty-2 function of 1/sin(1) over n^2.

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