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 1-10 of 11 results. Next

A145667 a(n) = number of components of the graph P(n,2) (defined in Comments).

Original entry on oeis.org

0, 1, 1, 2, 1, 2, 4, 11, 13, 19, 29, 43, 107, 169, 350, 603, 1134, 2070, 3803, 7502, 13989, 26495, 50826, 97369, 185827, 357307, 690577, 1332382, 2565110, 4958962, 9594425, 18569626, 36009794
Offset: 1

Views

Author

W. Edwin Clark, Mar 17 2009

Keywords

Comments

Let H(n,b) be the Hamming graph whose vertices are the sequences of length n over the alphabet {0,1,...,b-1} with adjacency being defined by having Hamming distance 1. Let P(n,b) be the subgraph of H(n,b) induced by the set of vertices which are base b representations of primes with n digits (not allowing leading 0 digits).

Crossrefs

Cf. A104080, A014234, A145668, A145669, A145670, A145671, A145672, A145673, A145674, A158576, A158577, A158578, A158579.

Extensions

a(18)-a(31) from Max Alekseyev, May 12 2011
a(32)-a(33) from Max Alekseyev, Dec 23 2024

A158576 a(n) = number of components of the graph P(n,10) (defined in Comments).

Original entry on oeis.org

1, 1, 1, 1, 1, 7, 38, 365, 3355, 33586
Offset: 1

Views

Author

W. Edwin Clark, Mar 21 2009

Keywords

Comments

Let H(n,b) be the Hamming graph whose vertices are the sequences of length n over the alphabet {0,1,...,b-1} with adjacency being defined by having Hamming distance 1. Let P(n,b) be the subgraph of H(n,b) induced by the set of vertices which are base b representations of primes with n digits (not allowing leading 0 digits).
For 6 and 7 digit primes there is a single large component and the remaining components have size 1. For 8 digit primes there is a single large component, the size 2 component {89391959, 89591959} and the remaining components have size 1. - W. Edwin Clark, Mar 31 2009
The elements of size 2 components in these graphs are sequence A253269. - Michael Kleber, May 04 2015

Examples

			The 6-digit primes 294001, 505447, 584141, 604171, 929573, 971767 (cf. A050249) have the property that changing any single digit always gives a composite number, so these are isolated nodes in the graph P(6,10) (which also has one large connected component).

Crossrefs

Cf. A050249, A145667, A145668, A145669, A145670, A145671, A145672, A145673, A145674, A158577, A158578, A158579, A253269.

Extensions

a(8) from W. Edwin Clark, Mar 31 2009
a(9)-a(10) from Max Alekseyev, Dec 23 2024

A145668 a(n) = size of the n-th term in S(2) (defined in Comments).

Original entry on oeis.org

2, 2, 1, 1, 5, 3, 4, 9, 2, 1, 1, 7, 4, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 12, 1, 20, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 29, 19, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 3, 1, 75, 2, 19, 4, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 23, 1, 82, 76, 1, 1, 3, 1, 1, 3, 3, 4, 2, 3, 3, 1, 2, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 9, 1, 2, 1, 1, 1, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1
Offset: 1

Views

Author

W. Edwin Clark, Mar 17 2009

Keywords

Comments

Let H(L,b) be the Hamming graph whose vertices are the sequences of length L over the alphabet {0,1,...,b-1} with adjacency being defined by having Hamming distance 1. Let P(L,b) be the subgraph of H(L,b) induced by the set of vertices which are base b representations of primes with L digits (not allowing leading 0 digits). Let S(b) be the sequence of all components of the graphs P(L,b), L>0, sorted by the smallest prime in a component.

Links

Crossrefs

Cf. A104080, A014234, A145667, A145669, A145670, A145671, A145672, A145673, A145674, A158576, A158577, A158578, A158579.

Extensions

More terms from Max Alekseyev, May 12 2011

A145670 a(n) = largest member of the n-th term in S(2) (defined in Comments).

Original entry on oeis.org

3, 7, 11, 13, 31, 61, 59, 113, 89, 107, 127, 227, 181, 173, 191, 229, 211, 223, 233, 239, 241, 251, 257, 479, 277, 503, 337, 349, 353, 373, 419, 431, 443, 491, 509, 619, 1021, 953, 557, 613, 653, 661, 683, 701, 709, 751, 733, 761, 773, 787, 853, 877, 971, 1019, 2029, 1123, 1879, 1409, 1163, 1699, 1193, 1201, 1259, 1381, 1433, 1451, 1453, 1553, 1597, 1637, 1913, 1709, 1979, 1753, 1759, 1777, 2039, 1811, 2017, 1907, 1931, 1973, 2027
Offset: 1

Views

Author

W. Edwin Clark, Mar 17 2009

Keywords

Comments

Let H(L,b) be the Hamming graph whose vertices are the sequences of length L over the alphabet {0,1,...,b-1} with adjacency being defined by having Hamming distance 1. Let P(L,b) be the subgraph of H(L,b) induced by the set of vertices which are base b representations of primes with L digits (not allowing leading 0 digits). Let S(b) be the sequence of all components of the graphs P(L,b), L>0, sorted by the smallest prime in a component.

Links

Crossrefs

Cf. A104080, A014234, A145667, A145668, A145669, A145671, A145672, A145673, A145674, A158576, A158577, A158578, A158579.

Extensions

More terms from Max Alekseyev, May 12 2011

A145672 a(n) = size of the n-th term in S(3) (defined in Comments).

Original entry on oeis.org

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

Views

Author

W. Edwin Clark, Mar 17 2009

Keywords

Comments

Let H(L,b) be the Hamming graph whose vertices are the sequences of length L over the alphabet {0,1,...,b-1} with adjacency being defined by having Hamming distance 1. Let P(L,b) be the subgraph of H(L,b) induced by the set of vertices which are base b representations of primes with L digits (not allowing leading 0 digits). Let S(b) be the sequence of all components of the graphs P(L,b), L>0, sorted by the smallest prime in a component.

Links

Crossrefs

Cf. A145667, A145668, A145669, A145670, A145671, A145673, A145674, A158576, A158577, A158578, A158579.

Extensions

More terms from Max Alekseyev, May 12 2011

A145673 a(n) = smallest member of the n-th term in S(3) (defined in Comments).

Original entry on oeis.org

2, 3, 7, 11, 13, 19, 23, 29, 31, 37, 41, 59, 61, 67, 71, 83, 97, 103, 109, 113, 149, 163, 167, 173, 191, 193, 199, 223, 229, 239, 251, 257, 271, 281, 283, 293, 307, 331, 337, 347, 353, 367, 373, 379, 389, 409, 421, 487, 491, 499, 503, 521, 523, 569, 571, 577, 599, 601, 607, 643, 659, 691, 733, 739, 743, 757, 761, 769, 773
Offset: 1

Views

Author

W. Edwin Clark, Mar 17 2009

Keywords

Comments

Let H(L,b) be the Hamming graph whose vertices are the sequences of length L over the alphabet {0,1,...,b-1} with adjacency being defined by having Hamming distance 1. Let P(L,b) be the subgraph of H(L,b) induced by the set of vertices which are base b representations of primes with L digits (not allowing leading 0 digits). Let S(b) be the sequence of all components of the graphs P(L,b), L>0, sorted by the smallest prime in a component.

Links

Crossrefs

Cf. A145667, A145668, A145669, A145670, A145671, A145672, A145674, A158576, A158577, A158578, A158579.

Extensions

More terms from Max Alekseyev, May 12 2011

A145674 a(n) = largest member of the n-th term in S(3) (defined in Comments).

Original entry on oeis.org

2, 5, 7, 17, 13, 19, 23, 53, 31, 43, 41, 59, 79, 67, 71, 137, 151, 157, 127, 131, 149, 181, 167, 233, 197, 211, 199, 241, 229, 239, 479, 419, 457, 449, 283, 293, 313, 349, 337, 401, 359, 367, 373, 397, 389, 463, 421, 727, 653, 661, 719, 701, 523, 647, 571, 631, 617, 619, 607, 643, 659, 691, 1453, 739, 1283, 1429, 761, 769
Offset: 1

Views

Author

W. Edwin Clark, Mar 17 2009

Keywords

Comments

Let H(L,b) be the Hamming graph whose vertices are the sequences of length L over the alphabet {0,1,...,b-1} with adjacency being defined by having Hamming distance 1. Let P(L,b) be the subgraph of H(L,b) induced by the set of vertices which are base b representations of primes with L digits (not allowing leading 0 digits). Let S(b) be the sequence of all components of the graphs P(L,b), L>0, sorted by the smallest prime in a component.

Links

Crossrefs

Cf. A145667, A145668, A145669, A145670, A145671, A145672, A145673, A158576, A158577, A158578, A158579.

Extensions

More terms from Max Alekseyev, May 12 2011

A158577 a(n) = size of the n-th term in S(10) (defined in Comments).

Original entry on oeis.org

4, 21, 143, 1061, 8363, 68900, 1, 1, 1, 1, 1, 1, 586044, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5096511, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
Offset: 1

Views

Author

W. Edwin Clark, Mar 21 2009

Keywords

Comments

Let H(L,b) be the Hamming graph whose vertices are the sequences of length L over the alphabet {0,1,...,b-1} with adjacency being defined by having Hamming distance 1. Let P(L,b) be the subgraph of H(L,b) induced by the set of vertices which are base b representations of primes with L digits (not allowing leading 0 digits). Let S(b) be the sequence of all components of the graphs P(L,b), L>0, sorted by the smallest prime in a component.
Next terms not equal 1: a(416) = 45082721 and a(3771) = 404171351 (see b-file). - Max Alekseyev, Dec 23 2024

Links

Crossrefs

Cf. A006879, A158576, A158578, A158579 (base 10).
Cf. A145667, A145668, A145669, A145670 (base 2).
Cf. A145671, A145672, A145673, A145674 (base 3).

Extensions

Terms a(51) onward from Max Alekseyev, Dec 23 2024

A158578 a(n) = smallest member of the n-th term in S(10) (defined in Comments).

Original entry on oeis.org

2, 11, 101, 1009, 10007, 100003, 294001, 505447, 584141, 604171, 929573, 971767, 1000003, 1062599, 1282529, 1524181, 2017963, 2474431, 2690201, 3070663, 3085553, 3326489, 4393139, 5152507, 5285767, 5564453, 5575259, 5974249, 6173731, 6191371, 6236179, 6463267, 6712591, 7204777, 7469789, 7469797, 7810223, 7858771, 7982543
Offset: 1

Views

Author

W. Edwin Clark, Mar 21 2009

Keywords

Comments

Let H(L,b) be the Hamming graph whose vertices are the sequences of length L over the alphabet {0,1,...,b-1} with adjacency being defined by having Hamming distance 1. Let P(L,b) be the subgraph of H(L,b) induced by the set of vertices which are base b representations of primes with L digits (not allowing leading 0 digits). Let S(b) be the sequence of all components of the graphs P(L,b), L>0, sorted by the smallest prime in a component.

Links

Crossrefs

Cf. A145667, A145668, A145669, A145670, A145671, A145672, A145673, A145674, A158576, A158577, A158579.

Extensions

Corrected and terms a(28) onward added by Max Alekseyev, Dec 23 2024

A158579 a(n) = largest member of the n-th term in S(10) (defined in Comments).

Original entry on oeis.org

7, 97, 997, 9973, 99991, 999983, 294001, 505447, 584141, 604171, 929573, 971767, 9999991, 1062599, 1282529, 1524181, 2017963, 2474431, 2690201, 3070663, 3085553, 3326489, 4393139, 5152507, 5285767, 5564453, 5575259, 5974249, 6173731, 6191371, 6236179, 6463267, 6712591, 7204777, 7469789, 7469797, 7810223, 7858771, 7982543, 8090057
Offset: 1

Views

Author

W. Edwin Clark, Mar 21 2009

Keywords

Comments

Let H(L,b) be the Hamming graph whose vertices are the sequences of length L over the alphabet {0,1,...,b-1} with adjacency being defined by having Hamming distance 1. Let P(L,b) be the subgraph of H(L,b) induced by the set of vertices which are base b representations of primes with L digits (not allowing leading 0 digits). Let S(b) be the sequence of all components of the graphs P(L,b), L>0, sorted by the smallest prime in a component.

Links

Crossrefs

Cf. A145667, A145668, A145669, A145670, A145671, A145672, A145673, A145674, A158576, A158577, A158578.

Extensions

Corrected and terms a(28) onward added by Max Alekseyev, Dec 23 2024
Showing 1-10 of 11 results. Next

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