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.

Showing 1-3 of 3 results.

A325445 Difference sequence of A325418.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 03 2019

Keywords

Comments

See A325417 for a guide to related sequences. Conjecture: all the differences are in {1,2,3,4,6}; 5 does not occur; a count of differences d(n) = a(n)-a(n-1) for n=2..10000 follows: 1082 occurrences of d(n) = 1; 2693 of 2; 744 of 3; 1609 of 4, 0 of 5, and 198 of 6.

Links

Crossrefs

Cf. A325417, A325444.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{#/2, (# - 1)/3}],
IntegerQ]]] &]], {2000}]; a ;       (* A325417 *)
c = Complement[Range[Last[a]], a] ; (* A325418 *)
Differences[a]  (* A325444 *)
Differences[c]  (* A325445 *)
(* Peter J. C. Moses, Apr 23 2019 *)

A325417 a(n) is the least number not 2*a(m) or 3*a(m)+1 for any m < n.

Original entry on oeis.org

1, 3, 5, 7, 8, 9, 11, 12, 13, 15, 17, 19, 20, 21, 23, 27, 29, 31, 32, 33, 35, 36, 39, 41, 43, 44, 45, 47, 48, 49, 50, 51, 53, 55, 56, 57, 59, 60, 63, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 89, 91, 92, 93, 95, 99, 101, 103, 104
Offset: 1

Views

Author

Clark Kimberling, Apr 24 2019

Keywords

Comments

In column 1 of the following guide to related sequences, disallowed terms are indicated by the variable x representing a(m) for m < n.
Disallowed Sequence(a) Complement(c) Differences(a) Differences(c)
2x, 3x+1 A325417 A325418 A325444 A325445
3x, 2x+1 A325419 A325420 A325494 A325495
2x+1, 3x+1 A077477 A325422 A325496 A325497
2x, 3x A036668 A325424 A325498 A325499
[3x/2], 2x A325425 A325426 A325518 A325519
[3x/2], 2x+1 A325427 A325428 A325520 A325521
[3x/2], 3x A325429 A325430 A325522 A325523
3x, 4x A325431 A325432 A325525 A325526
2x, 3x-1 A325462 A325463 A325526 A325527
2x, 3x-2 A325464 A325465 A325528 A325529
2x-1, 3x-1 A325440 A325441 A325530 A325531
2x-1, 3x A325442 A325443 A325532 A325533
2x+1, 3x+2 A325539 A325540 A325541 A325542

Examples

			The sequence necessarily starts with 1.  The next 2 terms are determined as follows:  because a(1) = 1, the numbers 2 and 4 are disallowed, so that a(2) = 3, whence the numbers 6 and 10 are disallowed, so that a(3) = 5.

Links

Crossrefs

Cf. A325418, A325444.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{#/2, (# - 1)/3}],
IntegerQ]]] &]], {150}]; a     (* A325417 *)
Complement[Range[Last[a]], a]  (* A325418 *)
(* Peter J. C. Moses, Apr 23 2019 *)

A325444 Difference sequence of A325417.

Original entry on oeis.org

2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 4, 2, 2, 1, 1, 2, 1, 3, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 4, 2, 2, 1, 1, 2, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 2, 2, 1
Offset: 1

Views

Author

Clark Kimberling, May 03 2019

Keywords

Comments

See A325417 for a guide to related sequences. Conjecture: all the differences are in {1,2,3,4}; a count of differences d(n) = a(n)-a(n-1) for n=2..10000 follows: 4755 occurrences of d(n) = 1; 4332 of 2; 744 of 3; and 169 of 4.

Examples

			A325417 is given by A(n) = least number not 2*A(m) or 3*A(m)+1 for any m < n, so that A = (1,3,5,7,8,9,11, ...), with differences (2,2,2,1,1,2,...).

Links

Crossrefs

Cf. A325417, A325445.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{#/2, (# - 1)/3}],
IntegerQ]]] &]], {2000}]; a ;       (* A325417 *)
c = Complement[Range[Last[a]], a] ; (* A325418 *)
Differences[a]  (* A325444 *)
Differences[c]  (* A325445 *)
(* Peter J. C. Moses, Apr 23 2019 *)
Showing 1-3 of 3 results.

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