A277568 -id:A277568 - cp's OEIS frontend

A277572 (1/2)*A277568.

1, 4, 6, 7, 10, 13, 16, 19, 22, 24, 25, 28, 31, 34, 36, 37, 40, 42, 43, 46, 49, 52, 55, 58, 60, 61, 64, 67, 70, 73, 76, 78, 79, 82, 85, 88, 91, 94, 96, 97, 100, 103, 106, 109, 112, 114, 115, 118, 121, 124, 127, 130, 132, 133, 136, 139, 142, 144, 145, 148

Offset: 1

Clark Kimberling, Nov 01 2016

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A277568, A277573, A277574.

z = 260; a[b_] := Table[Mod[n/b^IntegerExponent[n, b], b], {n, 1, z}]
p[b_, d_] := Flatten[Position[a[b], d]]
p[6, 2]/2 (* A277572 *)
p[6, 3]/3 (* A277573 *)
p[6, 4]/2 (* A277574 *)

A277569 Numbers k such that k/6^m == 3 (mod 6), where 6^m is the greatest power of 6 that divides k.

Original entry on oeis.org

3, 9, 15, 18, 21, 27, 33, 39, 45, 51, 54, 57, 63, 69, 75, 81, 87, 90, 93, 99, 105, 108, 111, 117, 123, 126, 129, 135, 141, 147, 153, 159, 162, 165, 171, 177, 183, 189, 195, 198, 201, 207, 213, 219, 225, 231, 234, 237, 243, 249, 255, 261, 267, 270, 273, 279

Offset: 1

Clark Kimberling, Nov 01 2016

Positions of 3 in A277544.
Numbers having 3 as rightmost nonzero digit in base 6.  This is one sequence in a 5-way splitting of the positive integers; the other four are indicated in the Mathematica program.  Every term is a multiple of 3; see A277573.
Numbers m having the property that tau(3m) < tau(2m) where tau(m) = A000005(m) (i.e., the number of divisors of m). - Gary Detlefs, Jan 28 2019

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A277544, A277567, A277568, A277573.

with(numtheory): for n from 1 to 279 do if tau(3*n)Gary Detlefs, Jan 28 2019

z = 260; a[b_] := Table[Mod[n/b^IntegerExponent[n, b], b], {n, 1, z}]
p[b_, d_] := Flatten[Position[a[b], d]]
p[6, 1] (* A277567 *)
p[6, 2] (* A277568 *)
p[6, 3] (* this sequence *)
p[6, 4] (* A277570 *)
p[6, 5] (* A277571 *)

is(n)=(n/6^valuation(n,6))%6==3 \\ Charles R Greathouse IV, Nov 03 2016

a(n) = 5n + O(log n). - Charles R Greathouse IV, Nov 03 2016

A277570 Numbers k such that k/6^m == 4 (mod 6), where 6^m is the greatest power of 6 that divides k.

Original entry on oeis.org

4, 10, 16, 22, 24, 28, 34, 40, 46, 52, 58, 60, 64, 70, 76, 82, 88, 94, 96, 100, 106, 112, 118, 124, 130, 132, 136, 142, 144, 148, 154, 160, 166, 168, 172, 178, 184, 190, 196, 202, 204, 208, 214, 220, 226, 232, 238, 240, 244, 250, 256, 262, 268, 274, 276, 280

Offset: 1

Clark Kimberling, Nov 01 2016

Positions of 4 in A277544.

Numbers having 4 as rightmost nonzero digit in base 6. This is one sequence in a 5-way splitting of the positive integers; the other four are indicated in the Mathematica program. Every term is even; see A277574.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A277544, A277567, A277571, A277574.

z = 260; a[b_] := Table[Mod[n/b^IntegerExponent[n, b], b], {n, 1, z}]
p[b_, d_] := Flatten[Position[a[b], d]]
p[6, 1] (* A277567 *)
p[6, 2] (* A277568 *)
p[6, 3] (* A277569 *)
p[6, 4] (* A277570 *)
p[6, 5] (* A277571 *)

is(n)=(n/6^valuation(n,6))%6==4 \\ Charles R Greathouse IV, Nov 03 2016

a(n) = 5n + O(log n). - Charles R Greathouse IV, Nov 03 2016

A277567 Numbers k such that k/6^m == 1 (mod 6), where 6^m is the greatest power of 6 that divides k.

Original entry on oeis.org

1, 6, 7, 13, 19, 25, 31, 36, 37, 42, 43, 49, 55, 61, 67, 73, 78, 79, 85, 91, 97, 103, 109, 114, 115, 121, 127, 133, 139, 145, 150, 151, 157, 163, 169, 175, 181, 186, 187, 193, 199, 205, 211, 216, 217, 222, 223, 229, 235, 241, 247, 252, 253, 258, 259, 265

Offset: 1

Clark Kimberling, Nov 01 2016

Positions of 1 in A277544. Numbers having 1 as rightmost nonzero digit in base 6. This is one sequence in a 5-way splitting of the positive integers; the other four are indicated in the Mathematica program.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A277544, A277568, A277569.

z = 260; a[b_] := Table[Mod[n/b^IntegerExponent[n, b], b], {n, 1, z}]
p[b_, d_] := Flatten[Position[a[b], d]]
p[6, 1] (* A277567 *)
p[6, 2] (* A277568 *)
p[6, 3] (* A277569 *)
p[6, 4] (* A277570 *)
p[6, 5] (* A277571 *)
Select[Range[300],Mod[#/6^IntegerExponent[#,6],6]==1&] (* Harvey P. Dale, Sep 27 2023 *)

is(n)=(n/6^valuation(n,6))%6==1 \\ Charles R Greathouse IV, Nov 03 2016

a(n) = 5n + O(log n). - Charles R Greathouse IV, Nov 03 2016

A277571 Numbers k such that k/6^m == 5 (mod 6), where 6^m is the greatest power of 6 that divides k.

Original entry on oeis.org

5, 11, 17, 23, 29, 30, 35, 41, 47, 53, 59, 65, 66, 71, 77, 83, 89, 95, 101, 102, 107, 113, 119, 125, 131, 137, 138, 143, 149, 155, 161, 167, 173, 174, 179, 180, 185, 191, 197, 203, 209, 210, 215, 221, 227, 233, 239, 245, 246, 251, 257, 263, 269, 275, 281

Offset: 1

Clark Kimberling, Nov 01 2016

Positions of 5 in A277544.

Numbers having 5 as rightmost nonzero digit in base 6. This is one sequence in a 5-way splitting of the positive integers; the other four are indicated in the Mathematica program.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A277544, A277567, A277570.

z = 260; a[b_] := Table[Mod[n/b^IntegerExponent[n, b], b], {n, 1, z}]
p[b_, d_] := Flatten[Position[a[b], d]]
p[6, 1] (* A277567 *)
p[6, 2] (* A277568 *)
p[6, 3] (* A277569 *)
p[6, 4] (* A277570 *)
p[6, 5] (* A277571 *)
Select[Range[300],Mod[#/6^IntegerExponent[#,6],6]==5&] (* Harvey P. Dale, Feb 14 2025 *)

is(n) = Mod(n/6^valuation(n, 6), 6)==5 \\ Felix Fröhlich, Nov 02 2016

a(n) = 5n + O(log n). - Charles R Greathouse IV, Nov 03 2016

A277573 a(n) = (1/3)*A277569(n).

Original entry on oeis.org

1, 3, 5, 6, 7, 9, 11, 13, 15, 17, 18, 19, 21, 23, 25, 27, 29, 30, 31, 33, 35, 36, 37, 39, 41, 42, 43, 45, 47, 49, 51, 53, 54, 55, 57, 59, 61, 63, 65, 66, 67, 69, 71, 73, 75, 77, 78, 79, 81, 83, 85, 87, 89, 90, 91, 93, 95, 97, 99, 101, 102, 103, 105, 107, 108

Offset: 1

Clark Kimberling, Nov 01 2016

From Amiram Eldar, Jan 16 2022: (Start)
Numbers whose 3-adic valuation is not smaller than their 2-adic valuation.
The asymptotic density of this sequence is 3/5. (End)

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A007814, A007949.

Cf. A277568, A277569, A277572, A277574.

z = 260; a[b_] := Table[Mod[n/b^IntegerExponent[n, b], b], {n, 1, z}]
p[b_, d_] := Flatten[Position[a[b], d]]
p[6, 3]/3
(* second program *)
Select[Range[200], IntegerExponent[#, 3] >= IntegerExponent[#, 2] &] (* Amiram Eldar, Jan 16 2022 *)

A277574 (1/2)*A277570.

Original entry on oeis.org

2, 5, 8, 11, 12, 14, 17, 20, 23, 26, 29, 30, 32, 35, 38, 41, 44, 47, 48, 50, 53, 56, 59, 62, 65, 66, 68, 71, 72, 74, 77, 80, 83, 84, 86, 89, 92, 95, 98, 101, 102, 104, 107, 110, 113, 116, 119, 120, 122, 125, 128, 131, 134, 137, 138, 140, 143, 146, 149, 152

Offset: 1

Clark Kimberling, Nov 01 2016

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A277568, A277572, A277573.

z = 260; a[b_] := Table[Mod[n/b^IntegerExponent[n, b], b], {n, 1, z}]
p[b_, d_] := Flatten[Position[a[b], d]]
p[6, 2]/2 (* A277572 *)
p[6, 3]/3 (* A277573 *)
p[6, 4]/2 (* A277574 *)

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A277572 (1/2)*A277568.

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A277569 Numbers k such that k/6^m == 3 (mod 6), where 6^m is the greatest power of 6 that divides k.

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A277570 Numbers k such that k/6^m == 4 (mod 6), where 6^m is the greatest power of 6 that divides k.

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A277567 Numbers k such that k/6^m == 1 (mod 6), where 6^m is the greatest power of 6 that divides k.

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A277571 Numbers k such that k/6^m == 5 (mod 6), where 6^m is the greatest power of 6 that divides k.

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A277573 a(n) = (1/3)*A277569(n).

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A277574 (1/2)*A277570.

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