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 1-7 of 7 results.

A288351 Number of strings of n digits from 1...9 such that no formula using the single digits in the given order exists that evaluates to 0.

Original entry on oeis.org

9, 72, 455, 1500, 1014, 181, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Hugo Pfoertner, Jun 08 2017

Keywords

Comments

For definitions and comments see A288350.
It is conjectured that a(n)=0 for n>=8.
The conjecture is true, as shown in the corresponding comment in A288350. - Hugo Pfoertner, Jun 09 2017

Examples

			a(1)=9 because 1...9 /=0. a(2)=72, because only the 9 numbers 11, 22, ..., 99 of the 81 two-digit strings can represent 0.

Crossrefs

Cf. A288350, A288352, A288353, A288354, A288355, A288356.

A288353 Strings of 3 digits from 1...9, such that no formula using the single digits in the given order exists that evaluates to 0.

Original entry on oeis.org

124, 125, 126, 127, 128, 129, 131, 135, 136, 137, 138, 139, 141, 142, 146, 147, 148, 149, 151, 152, 153, 157, 158, 159, 161, 162, 163, 164, 168, 169, 171, 172, 173, 174, 175, 179, 181, 182, 183, 184, 185, 186, 191, 192, 193, 194, 195, 196, 197, 214, 215, 216, 217, 218, 219, 232
Offset: 1

Views

Author

Hugo Pfoertner, Jun 08 2017

Keywords

Comments

For definitions and comments see A288350. The b-file provides all A288351(3)=455 sequence terms.

Links

Crossrefs

Cf. A288350, A288351, A288354, A288355, A288356.

A288354 Strings of 4 digits from 1...9, such that no formula using the single digits in the given order exists that evaluates to 0.

Original entry on oeis.org

1251, 1261, 1271, 1272, 1273, 1281, 1282, 1283, 1291, 1292, 1294, 1295, 1316, 1317, 1318, 1319, 1354, 1356, 1361, 1365, 1367, 1371, 1372, 1376, 1378, 1381, 1383, 1387, 1389, 1391, 1392, 1394, 1398, 1417, 1418, 1419, 1424, 1464, 1465, 1467, 1468, 1471, 1475, 1476, 1478, 1479, 1481, 1486, 1487, 1489, 1491, 1492, 1497, 1498
Offset: 1

Views

Author

Hugo Pfoertner, Jun 08 2017

Keywords

Comments

For definitions and comments see A288350. The b-file provides all A288351(4)=1500 sequence terms.

Links

Crossrefs

Cf. A288350, A288351, A288353, A288355, A288356.

A288355 Strings of 5 digits from 1...9, such that no formula using the single digits in the given order exists that evaluates to 0.

Original entry on oeis.org

12721, 12812, 13171, 13181, 13191, 13656, 13676, 13678, 13767, 13787, 13789, 13876, 13878, 13896, 13898, 13987, 13989, 14181, 14191, 14767, 14787, 14789, 14878, 14898, 14987, 14989, 15186, 15191, 15197, 15351, 15751, 15782, 15791, 15795, 15816, 15854, 15856, 15861, 15865
Offset: 1

Views

Author

Hugo Pfoertner, Jun 08 2017

Keywords

Comments

For definitions and comments see A288350. The b-file provides all A288351(5)=1014 sequence terms.

Links

Crossrefs

Cf. A288350, A288351, A288353, A288354, A288356.

A288356 Strings of 6 digits from 1...9, such that no formula using the single digits in the given order exists that evaluates to 0.

Original entry on oeis.org

169896, 174171, 174767, 174787, 185878, 185898, 191581, 191691, 194191, 194878, 194989, 195191, 195898, 195987, 195989, 196191, 196989, 565856, 569565, 595759, 658565, 673676, 674767, 676967, 698961, 714878, 767471, 767476, 769676, 783787, 783878, 785878, 787378, 787387, 789498, 814787, 814878
Offset: 1

Views

Author

Hugo Pfoertner, Jun 08 2017

Keywords

Comments

For definitions and comments see A288350. The b-file provides all A288351(6)=89 sequence terms.

Links

Crossrefs

Cf. A288350, A288351, A288353, A288354, A288355.

A288352 Number of strings of n digits from 1..9 such that a formula using the single digits in the given order with result 0 needs at least one division.

Original entry on oeis.org

0, 0, 5, 168, 659, 163, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Hugo Pfoertner, Jun 10 2017

Keywords

Comments

For definitions see A288350. An exhaustive computation for the 9^8 strings of 8 digits confirms that for all of them formulas avoiding divisions exist. a(8) = 0 implies that a(n) = 0 for n > 8.

Examples

			a(3)=5, because the 5 3-digit strings 263 (0=2-6/3), 284 (0=2-8/4), 362 (0=3-6/2), 393 (3-9/3), 482 (0=4-8/2) are the only ones of the 9^3-A288351(3)=274 3-digit strings for which a formula with result 0 exists that cannot avoid including a division.
A288502 provides a list of all strings with this property.

Crossrefs

Cf. A288350, A288351, A288502, A288550.

A288502 Strings of digits from 1...9 such that any possible formula using the single digits in the given order that evaluates to 0 needs to include at least one division.

Original entry on oeis.org

263, 284, 362, 393, 482, 1262, 1284, 1293, 1382, 1393, 1482, 1493, 1631, 1823, 1841, 1932, 1934, 2162, 2173, 2184, 2193, 2194, 2195, 2346, 2375, 2593, 2597, 2612, 2621, 2625, 2638, 2658, 2674, 2713, 2735, 2813, 2814, 2831, 2841, 2843, 2845, 2847, 2849, 2859, 2895, 2914
Offset: 1

Views

Author

Hugo Pfoertner, Jun 10 2017

Keywords

Comments

For definitions see A288350.

Examples

			1262 is in the sequence, because no formula with result 0 avoiding divisions can be found, but 0=1+2-(6/2). A file with examples of formulas for all sequence terms is provided, see link section.

Links

Crossrefs

Cf. A288350, A288352.
Showing 1-7 of 7 results.

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