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 1-4 of 4 results.

A309063 Numbers k such that, when computing A247476(k), all previous terms have been paired.

Original entry on oeis.org

1, 27, 33, 39, 115, 129, 141, 147, 153, 159, 165, 171, 177, 183, 189, 195, 201, 207, 213, 219, 225, 231, 237, 243, 249, 255, 261, 267, 979, 1017, 1297, 1303, 1309, 1315, 1321, 1327, 1333, 1339, 1345, 1351, 1357, 1363, 1369, 1375, 1381, 1387, 1393, 1399, 1405
Offset: 1

Views

Author

Rémy Sigrist, Jul 10 2019

Keywords

Comments

Apparently, the first difference of this sequence is unbounded.

Examples

			See illustration of first terms in Links section.

Links

Crossrefs

Cf. A247476.

Programs

  • C
    See Links section.

A309072 a(n) is the concatenation of the initial digit of A247476(k) for k = A309063(n)..A309063(n+1)-1.

Original entry on oeis.org

12132453674859161724822942, 121121, 121121, 2342536434553643455364345536436553789651617788966917178682392737988131273298, 78912142738493, 912112112192, 121121, 121121, 121121, 121121, 121121, 121121, 121121, 121121, 121121, 121121, 121121, 121121, 121121
Offset: 1

Views

Author

Rémy Sigrist, Jul 10 2019

Keywords

Comments

For any n > 0:
- a(n) has an even number of digits,
- for any digit d appearing in a(n):
- d appears an even number of times,
- each pair of digits d is separated by d other digits,
- a(n) cannot be split into two parts with these properties.
The distribution of the first million values is as follows:
Freq. Length Value
------ ------- --------------------------------------------------------------
932062 6 121121
44451 38 78912142778498923727318198971711218297
19557 12 891211211819
3915 12 912112112192
3 14 78912142738493
1 26 12132453674859161724822942
1 76 234253643455364345536434553643..966917178682392737988131273298
1 280 789121427784989237213188991211..392931211212392931211212392131
1 712 121322432234223322432234223322..819191717881219277988131273298
1 2200 789121427784989237213188991211..392931211212392931211212392131
1 6438 121322432234223322432234223322..798916167718196687792562387539
1 64958 121322432234223322432234223322..819191717881219277988131273298
1 112810 678912162768798916167718196687..687989161677181968971711218297
1 563478 121322432234223322432234223322..177669883476364987896612172869
1 744654 678912162768798916167718196687..819191717881219277988131273298
1 2095732 789121427784989237273181989712..392931211212392931211212392131
1 5830936 234253243252332243223422332243..177669883476364987896612172869

Examples

			For n = 2:
- A309063(2) = 27 and A309063(3)-1 = 32,
- A000030(A247476(27)) = A000030(13) = 1,
- A000030(A247476(28)) = A000030(25) = 2,
- A000030(A247476(29)) = A000030(14) = 1,
- A000030(A247476(30)) = A000030(15) = 1,
- A000030(A247476(31)) = A000030(26) = 2,
- A000030(A247476(32)) = A000030(16) = 1,
- hence a(2) = 121121.

Links

Crossrefs

Cf. A000030, A247476, A309063.

Programs

  • C
    See Links section.

A309073 Split the sequence A247476 into nonempty chunks of minimal length such that for d = 1..9, the number of terms with leading digit d is even; a(n) is the length of the n-th chunk.

Original entry on oeis.org

26, 6, 6, 76, 14, 12, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 712, 38, 280, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6
Offset: 1

Views

Author

Rémy Sigrist, Jul 10 2019

Keywords

Comments

This sequence corresponds to the first difference of A309063.

Examples

			See illustration of first terms in Links section.

Links

Crossrefs

Cf. A247476, A309063, A309072.

Formula

a(n) = A309063(n+1) - A309063(n).
a(n) = A055642(A309072(n)).

A342939 a(n) is the Skolem number of the triangular grid graph T_n.

Original entry on oeis.org

1, 2, 5, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436, 466, 497, 529, 562, 596, 631, 667, 704, 742, 781, 821, 862, 904, 947, 991, 1036, 1082, 1129, 1177, 1226, 1276, 1327, 1379, 1432, 1486
Offset: 1

Views

Author

Stefano Spezia, Mar 30 2021

Keywords

Comments

For the meaning of Skolem number of a graph, see Definitions 1.4 and 1.5 in Carrigan and Green.

Links

Crossrefs

Cf. A152947, A161680, A247476, A342938, A342940.
For n > 1, 3*A002061(n) gives the Skolem number of the hexagonal grid graph H_n.

Programs

  • Mathematica
    LinearRecurrence[{3,-3,1},{1,2,5,7,11,16},55]

Formula

O.g.f.: x*(1 - x + 2*x^2 - 3*x^3 + 3*x^4 - x^5)/(1 - x)^3.
E.g.f.: exp(x)*(2 + x^2)/2 - 1 + x^3/6.
a(n) = 3*a(n-1) - 3*a(n-2) - a(n-3) for n > 6.
Except for a(3) = 5:
a(n) = 1 + n*(n - 1)/2 (see Theorem 2.5 in Carrigan and Green).
a(n) = 1 + A161680(n).
a(n) = A152947(n-1).
Showing 1-4 of 4 results.

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