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.

A180679 Numbers with three distinct prime factors which when concatenated in any order form prime numbers.

Original entry on oeis.org

3311, 27181, 32153, 41237, 53977, 86507, 110971, 125069, 208579, 256413, 500981, 543337, 853811, 901949, 964481, 1053787, 1144171, 1197851, 1215731, 1344539, 1385189, 1433659, 1549603, 1674741, 1681547, 1699481, 1973479, 2028181
Offset: 1

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Author

James Farrington, Sep 15 2010

Keywords

Comments

The sequence admits only numbers with three distinct prime factors. A denser sequence (a superset) is obtained if prime factors may be repeated. [From R. J. Mathar, Oct 03 2010]
There is no term with four distinct prime factors under 10^8. [From Dmitri Kamenetsky, Sep 29 2012]

Examples

			For 3311, 3311=7 * 11 * 43, and 71143, 74311, 43711, 43117, 11437, 11743 are all prime numbers.

Crossrefs

Cf. A181559, A217263, A217264, A217265.

Programs

  • Mathematica
    Take[Union[Times @@@ Select[Subsets[Prime[Range[300]], {3}], And @@ PrimeQ[FromDigits /@ (Flatten /@ (IntegerDigits /@ Permutations[#]))] &]], 30] (* Harvey P. Dale, Jan 29 2011 *)

Extensions

Missing values inserted by R. J. Mathar, Oct 03 2010

A217263 Composite numbers such that every concatenation of their prime factors is prime.

Original entry on oeis.org

21, 33, 51, 63, 93, 111, 133, 177, 201, 219, 247, 253, 327, 411, 427, 549, 573, 589, 657, 679, 687, 763, 793, 813, 833, 889, 993, 1077, 1081, 1119, 1127, 1243, 1339, 1347, 1401, 1411, 1497, 1501, 1603, 1623, 1651, 1671, 1821, 1839, 1843, 1851, 1981, 2009, 2019
Offset: 1

Views

Author

Dmitri Kamenetsky, Sep 29 2012

Keywords

Comments

The smallest term with 3 or more prime factors is 63 = 3*3*7 (see A217264).
The smallest term with 4 or more prime factors is 21249 = 3*3*3*787 (see A217265).
The smallest term with 5 or more prime factors is 146461 = 7*7*7*7*61.
There is no term under 10^8 with 6 or more prime factors.
The smallest term with 3 or more distinct prime factors is 3311 = 7*11*43 (see A180679).
There is no term under 10^8 with 4 or more distinct prime factors.

Examples

			21 is 3*7. Both 37 and 73 are prime, so 21 is in the sequence.
63 is 3*3*7. 337, 373 and 733 are all prime, so 63 is in the sequence.

Crossrefs

Cf. A217264, A217265, A180679, A181559. Related sequences: A105184, A019549 and A106582.

A217264 Numbers with 3 or more prime factors (with multiplicity) such that every concatenation of their prime factors is prime.

Original entry on oeis.org

63, 549, 657, 833, 1127, 2009, 3311, 3971, 4149, 5043, 5409, 5491, 10539, 11493, 13059, 13941, 14517, 16839, 17591, 17991, 18621, 19133, 20259, 20781, 21119, 21249, 21537, 22023, 23471, 24183, 25529, 27181, 30897, 31653, 32153, 33271, 33309, 34227, 35443
Offset: 1

Views

Author

Dmitri Kamenetsky, Sep 29 2012

Keywords

Examples

			63 is 3*3*7. 337, 373 and 733 are all prime, so 63 is in the sequence.

Crossrefs

Cf. A217263, A217265, A180679, A181559.

A217265 Numbers with 4 or more prime factors (with multiplicity) such that every concatenation of their prime factors is prime.

Original entry on oeis.org

21249, 33271, 89937, 146461, 147833, 148519, 164297, 175257, 211631, 216953, 234269, 254849, 261023, 269941, 311229, 318033, 348823, 377001, 390447, 520209, 561491, 848239, 941679, 943679, 957447, 960957, 1012879, 1110159, 1221431, 1410399, 1525203, 1681729
Offset: 1

Views

Author

Dmitri Kamenetsky, Sep 29 2012

Keywords

Examples

			21249 is 3*3*3*787. 333787, 337873, 378733 and 787333 are all prime, so 21249 is in the sequence.

Crossrefs

Cf. A217263, A217264, A180679, A181559.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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