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 1-6 of 6 results.

A055187 Cumulative counting sequence: method A (adjective-before-noun)-pairs with first term 1.

Original entry on oeis.org

1, 1, 1, 3, 1, 4, 1, 1, 3, 6, 1, 2, 3, 1, 4, 8, 1, 1, 2, 3, 3, 2, 4, 1, 6, 11, 1, 3, 2, 5, 3, 3, 4, 2, 6, 1, 8, 13, 1, 5, 2, 8, 3, 4, 4, 1, 5, 3, 6, 2, 8, 1, 11, 16, 1, 7, 2, 10, 3, 6, 4, 3, 5, 4, 6, 4, 8, 2, 11, 1, 13, 18, 1, 9, 2, 12, 3, 9, 4, 4, 5, 6, 6, 1, 7, 5, 8, 1, 10, 3, 11, 2, 13, 1, 16, 22, 1
Offset: 1

Views

Author

Clark Kimberling, Apr 27 2000

Keywords

Comments

Conjectures: limit as n goes to infinity of max {a(k) : 1<=k<=n}/sqrt(n) = 2;
-3 < a(n) - 2*sqrt(n) < 3 for all n;
there are infinitely many n such that a(n)=a(n+1). - Benoit Cloitre, Jan 30 2003
After starting with 1, successive segments are generated in adjective-before-noun pairs as in A055186 (i.e., the noun-integers are in increasing order). See A217780 for the sequence originally placed here, in which the noun-integers are in order of 1st occurrence. - Clark Kimberling, Mar 24 2013

Examples

			After writing 1, pairs, written vertically, are as shown:
1..1..3..4 1..6 2 1..8 1 3 2 1..
...1..1..1 3..1 3 4..1 2 3 4 6..

Links

Crossrefs

Cf. A055186, A217780.

Programs

  • Mathematica
    s = {1}; Do[s = Flatten[{s, {Count[s, #], #} & /@ Union[s]}], {14}]; s  (* A055187 *) (* Peter J. C. Moses, Mar 21 2013 *)

Extensions

Corrected and extended by Benoit Cloitre, Jan 30 2003

A055191 Cumulative counting sequence: method A (adjective-before-noun) pairs, starting with 5.

Original entry on oeis.org

5, 1, 5, 2, 5, 1, 1, 3, 5, 3, 1, 1, 2, 4, 5, 5, 1, 2, 2, 2, 3, 6, 5, 6, 1, 5, 2, 3, 3, 1, 4, 8, 5, 8, 1, 6, 2, 5, 3, 2, 4, 2, 6, 10, 5, 9, 1, 9, 2, 6, 3, 3, 4, 4, 6, 2, 8, 11, 5, 10, 1, 11, 2, 8, 3, 5, 4, 6, 6, 3, 8, 1, 10, 2, 9, 13, 5, 12, 1, 13, 2, 10, 3, 6, 4, 8
Offset: 1

Views

Author

Clark Kimberling, Apr 27 2000

Keywords

Comments

Segments (generated as at A217760): 5; 1,5; 2,5,1,1; 3,5,3,1,1,2; ... The 4th segment is read "3 5's and 3 1's and 1 2" as a record of what was previously written; 3,3,1 are adjectives and 5 1 2 are nouns. Conjecture: every nonnegative integer occurs. - Clark Kimberling, Mar 25 2013

Examples

			Write 5, thus having 1 5, thus having 2 5's and 1 1, thus having 3 5's and 3 1's and 1 2, etc.

Links

Crossrefs

Cf. A217760, A217780.

Programs

  • Mathematica
    s = {5}; Do[s = Flatten[{s, {Count[s, #], #} & /@ DeleteDuplicates[s]}], {14}]; s (* Peter J. C. Moses, Mar 21 2013 *)

A055190 Cumulative counting sequence: method A (adjective-before-noun) pairs, starting with 4.

Original entry on oeis.org

4, 1, 4, 2, 4, 1, 1, 3, 4, 3, 1, 1, 2, 4, 4, 5, 1, 2, 2, 2, 3, 6, 4, 6, 1, 5, 2, 3, 3, 1, 5, 7, 4, 8, 1, 6, 2, 5, 3, 3, 5, 2, 6, 8, 4, 9, 1, 8, 2, 7, 3, 5, 5, 4, 6, 1, 7, 1, 8, 10, 4, 12, 1, 9, 2, 8, 3, 7, 5, 5, 6, 3, 7, 4, 8, 1, 9, 12, 4, 14, 1, 10, 2, 10, 3, 9, 5, 6
Offset: 1

Views

Author

Clark Kimberling, Apr 27 2000

Keywords

Comments

Segments (as at A217760): 4; 1,4; 2,4,1,1; 3,4,3,1,1,2; ...
The 4th segment is read "3 4's and 3 1's and 1 2" as a record of what was previously written; 3,3,1 are adjectives and 4 1 2 are nouns. Conjecture: every nonnegative integer occurs. - Clark Kimberling, Mar 25 2013

Examples

			Write 4, thus having 1 4, thus having 2 4's and 1 1, thus having 3 4's and 3 1's and 1 2, etc.

Links

Crossrefs

Cf. A217760, A217780.

Programs

  • Mathematica
    s = {4}; Do[s = Flatten[{s, {Count[s, #], #} & /@ DeleteDuplicates[s]}], {14}]; s (* Peter J. C. Moses, Mar 21 2013 *)

A358066 Inventory sequence: record where the 1's, 2's, etc. are located starting with a(1) = 1, a(2) = 1 (see example).

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 3, 4, 1, 2, 3, 5, 4, 6, 7, 1, 2, 3, 5, 9, 4, 6, 10, 7, 11, 8, 13, 1, 2, 3, 5, 9, 16, 4, 6, 10, 17, 7, 11, 18, 8, 13, 21, 12, 19, 1, 2, 3, 5, 9, 16, 28, 4, 6, 10, 17, 29, 7, 11, 18, 30, 8, 13, 21, 34, 12, 19, 31, 14, 22, 35, 1, 2, 3, 5, 9, 16, 28, 46, 4, 6, 10, 17, 29, 47, 7, 11, 18, 30, 48
Offset: 1

Views

Author

Ctibor O. Zizka, Oct 29 2022

Keywords

Examples

			At stage n >= 1 we only look at the numbers 1 up to n, and ignore numbers bigger than n.
Stage 0: start with a(1) = 1, a(2) = 1.
Stage 1: we see 1's at 1,2, so we adjoin 1,2, getting 1,1, 1,2.
Stage 2: we see 1's at 1,2,3, and 2's at 4, so we adjoin 1,2,3,4, getting 1,1,1,2, 1,2,3,4.
Stage 3: we see 1's at 1,2,3,5, 2's at 4,6 and 3's at 7, so we adjoin 1,2,3,5,4,6,7, getting 1,1,1,2,1,2,3,4, 1,2,3,5,4,6,7.
Stage 4: we see 1's at 1,2,3,5,9, 2's at 4,6,10, 3's at 7,11, 4's at 8,13, so we adjoin 1,2, ..., 8,13 and so on.
We obtain an irregular triangle by writing the results of the stages as separate rows:
1, 1,
1, 2,
1, 2, 3, 4,
1, 2, 3, 5, 4, 6, 7,
1, 2, 3, 5, 9, 4, 6, 10, 7, 11, 8, 13,
1, 2, 3, 5, 9, 16, 4, 6, 10, 17, 7, 11, 18, 8, 13, 21, 12, 19,
1, 2, 3, 5, 9, 16, 28, 4, 6, 10, 17, 29, 7, 11, 18, 30, 8, 13, 21, 34, 12, 19, 31, 14, 22, 35,
... (_N. J. A. Sloane_, Nov 07 2022)

Crossrefs

See A357443 for another version.
Cf. A030717, A055187, A217780, A342585, A357317, A356784.

Programs

  • Python
    terms = [1, 1]
for i in range(1,11):
    new_terms = []
    for j in range(1, i+1):
        for k in range(len(terms)):
            if terms[k] == j: new_terms.append(k+1)
    terms.extend(new_terms)
print(terms) # Gleb Ivanov, Nov 01 2022

A055188 Cumulative counting sequence: method A (adjective-before-noun) pairs, starting with 2.

Original entry on oeis.org

2, 1, 2, 2, 2, 1, 1, 4, 2, 3, 1, 5, 2, 4, 1, 1, 4, 1, 3, 6, 2, 7, 1, 3, 4, 2, 3, 1, 5, 8, 2, 9, 1, 4, 4, 4, 3, 2, 5, 1, 6, 1, 7, 10, 2, 12, 1, 7, 4, 5, 3, 3, 5, 2, 6, 2, 7, 1, 8, 1, 9, 13, 2, 15, 1, 8, 4, 7, 3, 5, 5, 3, 6, 4, 7, 2, 8, 2, 9, 1, 10, 1, 12, 16, 2, 18
Offset: 1

Views

Author

Clark Kimberling, Apr 27 2000

Keywords

Comments

Segments (generated as at A217760): 2; 1,2; 2,2,1,1; 4,2,3,1; 5,2,4,1,1,4,1,3; ... The 4th segment is read "4 2's and 3 1's" as a record of what was previously written; 4,2 are adjectives and 2 1 are nouns. Conjecture: every nonnegative integer occurs. - Clark Kimberling, Mar 25 2013

Examples

			Write 2, thus having 1 2, thus having 2 2's and 1 1, thus having 4 2's and 3 1's, etc.

Links

Crossrefs

Cf. A217760, A217780.

Programs

  • Mathematica
    s = {2}; Do[s = Flatten[{s, {Count[s, #], #} & /@ DeleteDuplicates[s]}], {14}]; s (* Peter J. C. Moses, Mar 21 2013 *)

A055189 Cumulative counting sequence: method A (adjective-before-noun)-pairs, starting with 3.

Original entry on oeis.org

3, 1, 3, 2, 3, 1, 1, 3, 3, 3, 1, 1, 2, 6, 3, 5, 1, 2, 2, 7, 3, 6, 1, 4, 2, 1, 6, 1, 5, 8, 3, 9, 1, 5, 2, 3, 6, 2, 5, 1, 7, 1, 4, 10, 3, 12, 1, 7, 2, 4, 6, 4, 5, 2, 7, 2, 4, 1, 8, 1, 9, 11, 3, 15, 1, 10, 2, 5, 6, 5, 5, 4, 7, 5, 4, 2, 8, 2, 9, 1, 10, 1, 12, 12, 3, 18
Offset: 1

Views

Author

Clark Kimberling, Apr 27 2000

Keywords

Comments

Segments (generated as at A217760): 3; 1,3; 2,3,1,1; 3,3,3,1,1,2; ...
The 4th segment is read "3 3's and 3 1's and 1 2" as a record of what was previously written; 3 3 1 are adjectives and 3 1 2 are nouns. Conjecture: every nonnegative integer occurs. - Clark Kimberling, Mar 25 2013

Examples

			Write 3, thus having 1 3, thus having 2 3's and 1 1, thus having 3 3's and 3 1's and 1 2, etc.

Links

Crossrefs

Cf. A217760, A217780.

Programs

  • Mathematica
    s = {3}; Do[s = Flatten[{s, {Count[s, #], #} & /@ DeleteDuplicates[s]}], {14}]; s (* Peter J. C. Moses, Mar 21 2013 *)
Showing 1-6 of 6 results.

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