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 11-20 of 90 results. Next

A297231 Down-variation of the base-11 digits of n; see Comments.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jan 17 2018

Keywords

Comments

Suppose that a number n has base-b digits b(m), b(m-1), ..., b(0). The base-b down-variation of n is the sum DV(n,b) of all d(i)-d(i-1) for which d(i) > d(i-1); the base-b up-variation of n is the sum UV(n,b) of all d(k-1)-d(k) for which d(k) < d(k-1). The total base-b variation of n is the sum TV(n,b) = DV(n,b) + UV(n,b). Every positive integer occurs infinitely many times. See A297330 for a guide to related sequences and partitions of the natural numbers.

Examples

			22 in base 11: 2,0; here DV = 2, so that a(22) = 2.

Links

Crossrefs

Cf. A297232, A297233, A297330.

Programs

  • Mathematica
    g[n_, b_] := Differences[IntegerDigits[n, b]];
b = 11; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297231 *)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297232 *)

A297232 Up-variation of the base-11 digits of n; see Comments.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2
Offset: 1

Views

Author

Clark Kimberling, Jan 17 2018

Keywords

Comments

Suppose that a number n has base-b digits b(m), b(m-1), ..., b(0). The base-b down-variation of n is the sum DV(n,b) of all d(i)-d(i-1) for which d(i) > d(i-1); the base-b up-variation of n is the sum UV(n,b) of all d(k-1)-d(k) for which d(k) < d(k-1). The total base-b variation of n is the sum TV(n,b) = DV(n,b) + UV(n,b). Every positive integer occurs infinitely many times. See A297330 for a guide to related sequences and partitions of the natural numbers.

Examples

			15 in base 11: 1,4; here UV = 3, so that a(15) = 3.

Links

Crossrefs

Cf. A297231, A297233, A297330.

Programs

  • Mathematica
    g[n_, b_] := Differences[IntegerDigits[n, b]];
b = 11; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297231 *)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297232 *)

A297233 Total variation of base-11 digits of n; see Comments.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2
Offset: 1

Views

Author

Clark Kimberling, Jan 17 2018

Keywords

Comments

Suppose that a number n has base-b digits b(m), b(m-1), ..., b(0). The base-b down-variation of n is the sum DV(n,b) of all d(i)-d(i-1) for which d(i) > d(i-1); the base-b up-variation of n is the sum UV(n,b) of all d(k-1)-d(k) for which d(k) < d(k-1). The total base-b variation of n is the sum TV(n,b) = DV(n,b) + UV(n,b). See A297330 for a guide to related sequences and partitions of the natural numbers:

Examples

			2^20 in base 11:  6, 5, 6, 8, 10, 1; here, DV = 12 and UV = 5, so that a(2^20) = 17.

Links

Crossrefs

Cf. A297231, A297232, A297330.

Programs

  • Mathematica
    b = 11; z = 120; t = Table[Total@Flatten@Map[Abs@Differences@# &,      Partition[IntegerDigits[n, b], 2, 1]], {n, z}] (* cf. Michael De Vlieger, e.g. A037834 *)

A297234 Down-variation of the base-12 digits of n; see Comments.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jan 17 2018

Keywords

Comments

Suppose that a number n has base-b digits b(m), b(m-1), ..., b(0). The base-b down-variation of n is the sum DV(n,b) of all d(i)-d(i-1) for which d(i) > d(i-1); the base-b up-variation of n is the sum UV(n,b) of all d(k-1)-d(k) for which d(k) < d(k-1). The total base-b variation of n is the sum TV(n,b) = DV(n,b) + UV(n,b). Every positive integer occurs infinitely many times. See A297330 for a guide to related sequences and partitions of the natural numbers.

Examples

			24 in base 12: 2,0; here DV = 2, so that a(24) = 2.

Links

Crossrefs

Cf. A297234, A297235, A297330.

Programs

  • Mathematica
    g[n_, b_] := Differences[IntegerDigits[n, b]];
b = 12; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297234 *)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297235 *)

A297235 Up-variation of the base-12 digits of n; see Comments.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 0, 0, 0
Offset: 1

Views

Author

Clark Kimberling, Jan 17 2018

Keywords

Comments

Suppose that a number n has base-b digits b(m), b(m-1), ..., b(0). The base-b down-variation of n is the sum DV(n,b) of all d(i)-d(i-1) for which d(i) > d(i-1); the base-b up-variation of n is the sum UV(n,b) of all d(k-1)-d(k) for which d(k) < d(k-1). The total base-b variation of n is the sum TV(n,b) = DV(n,b) + UV(n,b). Every positive integer occurs infinitely many times. See A297330 for a guide to related sequences and partitions of the natural numbers.

Examples

			16 in base 12: 1,4; here UV = 3, so that a(16) = 3.

Links

Crossrefs

Cf. A297234, A297235, A297330.

Programs

  • Mathematica
    g[n_, b_] := Differences[IntegerDigits[n, b]];
b = 12; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297234 *)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297235 *)

A297237 Down-variation of the base-13 digits of n; see Comments.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 6, 5, 4, 3, 2, 1, 0, 0, 0
Offset: 1

Views

Author

Clark Kimberling, Jan 17 2018

Keywords

Comments

Suppose that a number n has base-b digits b(m), b(m-1), ..., b(0). The base-b down-variation of n is the sum DV(n,b) of all d(i)-d(i-1) for which d(i) > d(i-1); the base-b up-variation of n is the sum UV(n,b) of all d(k-1)-d(k) for which d(k) < d(k-1). The total base-b variation of n is the sum TV(n,b) = DV(n,b) + UV(n,b). Every positive integer occurs infinitely many times. See A297330 for a guide to related sequences and partitions of the natural numbers.

Examples

			26 in base 13: 2,0; here DV = 2, so that a(26) = 2.

Links

Crossrefs

Cf. A297238, A297239, A297330.

Programs

  • Mathematica
    g[n_, b_] := Differences[IntegerDigits[n, b]];
b = 13; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297237 *)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297238 *)

A297238 Up-variation of the base-13 digits of n; see Comments.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 0, 0, 0, 0, 0, 0, 0, 1
Offset: 1

Views

Author

Clark Kimberling, Jan 17 2018

Keywords

Comments

Suppose that a number n has base-b digits b(m), b(m-1), ..., b(0). The base-b down-variation of n is the sum DV(n,b) of all d(i)-d(i-1) for which d(i) > d(i-1); the base-b up-variation of n is the sum UV(n,b) of all d(k-1)-d(k) for which d(k) < d(k-1). The total base-b variation of n is the sum TV(n,b) = DV(n,b) + UV(n,b). Every positive integer occurs infinitely many times. See A297330 for a guide to related sequences and partitions of the natural numbers.

Examples

			17 in base 13: 1,4; here UV = 3, so that a(17) = 3.

Links

Crossrefs

Cf. A297237, A297239, A297330.

Programs

  • Mathematica
    g[n_, b_] := Differences[IntegerDigits[n, b]];
b = 13; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297237 *)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297238 *)

A297239 Total variation of base-13 digits of n; see Comments.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 0, 1
Offset: 1

Views

Author

Clark Kimberling, Jan 17 2018

Keywords

Comments

Suppose that a number n has base-b digits b(m), b(m-1), ..., b(0). The base-b down-variation of n is the sum DV(n,b) of all d(i)-d(i-1) for which d(i) > d(i-1); the base-b up-variation of n is the sum UV(n,b) of all d(k-1)-d(k) for which d(k) < d(k-1). The total base-b variation of n is the sum TV(n,b) = DV(n,b) + UV(n,b). See A297330 for a guide to related sequences and partitions of the natural numbers:

Examples

			2^20 in base 13:  2, 10, 9, 3, 7, 9; here, DV = 12 and UV = 9, so that a(2^20) = 21.

Links

Crossrefs

Cf. A297237, A297238, A297330.

Programs

  • Mathematica
    b = 13; z = 120; t = Table[Total@Flatten@Map[Abs@Differences@# &,      Partition[IntegerDigits[n, b], 2, 1]], {n, z}] (* cf. Michael De Vlieger, e.g. A037834 *)

A297240 Down-variation of the base-14 digits of n; see Comments.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 5, 4
Offset: 1

Views

Author

Clark Kimberling, Jan 17 2018

Keywords

Comments

Suppose that a number n has base-b digits b(m), b(m-1), ..., b(0). The base-b down-variation of n is the sum DV(n,b) of all d(i)-d(i-1) for which d(i) > d(i-1); the base-b up-variation of n is the sum UV(n,b) of all d(k-1)-d(k) for which d(k) < d(k-1). The total base-b variation of n is the sum TV(n,b) = DV(n,b) + UV(n,b). Every positive integer occurs infinitely many times. See A297330 for a guide to related sequences and partitions of the natural numbers.

Examples

			28 in base 14: 2,0; here DV = 2, so that a(28) = 2.

Links

Crossrefs

Cf. A297241, A297242, A297330.

Programs

  • Mathematica
    g[n_, b_] := Differences[IntegerDigits[n, b]];
b = 14; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297240 *)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297241 *)

A297241 Up-variation of the base-14 digits of n; see Comments.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0
Offset: 1

Views

Author

Clark Kimberling, Jan 17 2018

Keywords

Comments

Suppose that a number n has base-b digits b(m), b(m-1), ..., b(0). The base-b down-variation of n is the sum DV(n,b) of all d(i)-d(i-1) for which d(i) > d(i-1); the base-b up-variation of n is the sum UV(n,b) of all d(k-1)-d(k) for which d(k) < d(k-1). The total base-b variation of n is the sum TV(n,b) = DV(n,b) + UV(n,b). Every positive integer occurs infinitely many times. See A297330 for a guide to related sequences and partitions of the natural numbers.

Examples

			18 in base 14: 1,4; here UV = 3, so that a(18) = 3.

Links

Crossrefs

Cf. A297240, A297242, A297330.

Programs

  • Mathematica
    g[n_, b_] := Differences[IntegerDigits[n, b]];
b = 14; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297240 *)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297241 *)
Previous Showing 11-20 of 90 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.