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.

User: Ki Punches

Ki Punches's wiki page.

Ki Punches has authored 58 sequences. Here are the ten most recent ones:

A156113 Seven-digit primes that begin with 1 followed by permutations of digits 2 to 7.

Original entry on oeis.org

1234657, 1245763, 1246537, 1246573, 1247563, 1254367, 1254637, 1256347, 1257463, 1263547, 1264537, 1264573, 1265347, 1275643, 1276543, 1324567, 1342567, 1342657, 1345627, 1354267, 1356247, 1356427, 1362457, 1425367
Offset: 1

Views

Author

Ki Punches, Mar 15 2009

Keywords

Comments

Sequence is finite, final term a(63)=1764253.
The full list is:
1234657,1245763,1246537,1246573,1247563,1254367,1254637,
1256347,1257463,1263547,1264537,1264573,1265347,1275643,
1276543,1324567,1342567,1342657,1345627,1354267,1356247,
1356427,1362457,1425367,1426753,1427563,1427653,1435627,
1436257,1436527,1452637,1453267,1463257,1465273,1476253,
1476523,1524637,1524763,1532647,1546273,1546327,1562347,
1563427,1564237,1572643,1574623,1576243,1624573,1625347,
1632457,1634257,1645327,1647253,1647523,1652347,1653427,
1672453,1674523,1725463,1726453,1742563,1752643,1764253.

Crossrefs

Cf. A156119.

Programs

  • Mathematica
    Select[10^6+FromDigits/@Permutations[Range[2,7]],PrimeQ] (* Zak Seidov, Dec 18 2010 *)

Extensions

Corrected by Ray Chandler, May 25 2009

A157410 Final primes in successive prime centuries.

Original entry on oeis.org

97, 199, 293, 397, 499, 599, 691, 797, 887, 997, 1097, 1193, 1297, 1399, 1499, 1597, 1699, 1789, 1889, 1999, 2099, 2179, 2297, 2399, 2477, 2593, 2699, 2797, 2897, 2999, 3089, 3191, 3299, 3391, 3499, 3593, 3697, 3797, 3889, 3989, 4099, 4177, 4297, 4397
Offset: 1

Views

Author

Ki Punches, Feb 28 2009

Keywords

Crossrefs

A157338 for first primes in prime centuries.

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Aug 20 2013

A157717 Primes that start a run of at least seven consecutive primes, where between successive primes exactly one digit changes and the resulting digits may be permuted.

Original entry on oeis.org

311, 401, 613, 811, 1013, 1471, 1861, 2011, 4051, 4261, 4801, 4903, 6067, 8209, 8501, 9403, 9461, 10061, 10301, 11831, 13913, 14051, 19961, 20353, 20707, 22063, 25031, 25903, 27763, 31511, 36313, 37561, 43313, 43517, 49003, 49331, 49891, 51817
Offset: 1

Views

Author

Ki Punches, Mar 04 2009, Mar 06 2009

Keywords

Comments

One and only one digit can change between any two successive primes in a run.
Rearrangement is optionally permitted to arrive at next consecutive prime in run.
Leading zeros are not permitted; all numbers in the run must have the same number of digits.

Examples

			311 is in the sequence because it begins a run of seven consecutive primes as required:
311 (1->3) 313 (3->7) 317 (7->3,swap 1&3) 331 (1->7) 337 (3->4) 347 (7->9) 349.
401 starts a run of nine: 401, 409, 419, 421, 431, 433, 439, 443, 449.
Note that 409 and 419 are not included since they are not the start of the run.

Crossrefs

Cf. A157885.

Extensions

Edited by Ray Chandler, Mar 08 2009

A157747 Consecutive prime pairs with common start/end decimal digits.

Original entry on oeis.org

181, 191, 787, 797, 919, 929, 1021, 1031, 1051, 1061, 1171, 1181, 1471, 1481, 1801, 1811, 3413, 3433, 3583, 3593, 3823, 3833, 3853, 3863, 7177, 7187, 7297, 7307, 7507, 7517, 9049, 9059, 9679, 9689, 10141, 10151, 10321, 10331, 10771, 10781, 11161
Offset: 1

Views

Author

Ki Punches, Mar 15 2009

Keywords

Extensions

1471, 1481, 3853, 3863 inserted by Ray Chandler, May 23 2009

A157967 Least prime of prime quadruplets that are separated by 210 or less from another least prime of prime quadruplet.

Original entry on oeis.org

5, 11, 101, 191, 1871, 2081, 3251, 3461, 15641, 15731, 397541, 397751, 1006301, 1006331, 1022381, 1022501, 1117601, 1117811, 1246241, 1246361, 1954151, 1954361, 2594951, 2594981, 2731691, 2731901, 2927591, 2927801, 3512051, 3512231
Offset: 1

Views

Author

Ki Punches, Mar 10 2009

Keywords

Examples

			{5,11}, {11,101} and {101,191} are pairs of least primes of prime quadruplets that are separated by 210 or less, so 5, 11, 101 and 191 are in sequence.

Crossrefs

Subsequence of A007530.

Extensions

Corrected final two sequence terms. Ki Punches, May 01 2009
Edited and corrected by Ray Chandler, May 24 2009

A158209 The number of consecutive prime pairs with 10-gap in n-th century.

Original entry on oeis.org

0, 2, 2, 1, 2, 2, 1, 2, 2, 1, 3, 2, 1, 0, 1, 0, 1, 1, 2, 0, 4, 1, 0, 0, 0, 1, 1, 3, 1, 1, 1, 1, 0, 1, 0, 4, 0, 2, 2, 0, 0, 0, 6, 3, 1, 0, 1, 0, 1, 2, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 3, 2, 3, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 1, 1, 2, 2, 0, 2, 0, 0, 2, 1, 1, 0, 1, 0, 2, 1, 1, 0, 0, 1, 1, 1, 0, 2, 1
Offset: 1

Views

Author

Ki Punches, Mar 13 2009

Keywords

Examples

			Of 14 primes in 10th century, only 919 and 929 are consecutive primes with 10-gap, so a(10)=1.

Extensions

Edited and corrected by Ray Chandler, May 23 2009

A158861 The lesser of twin prime pairs with each prime in a different millennia.

Original entry on oeis.org

2999, 8999, 101999, 164999, 179999, 230999, 272999, 293999, 326999, 389999, 410999, 419999, 443999, 512999, 524999, 536999, 659999, 662999, 773999, 788999, 794999, 800999, 818999, 890999, 920999, 932999, 989999, 1028999, 1058999, 1136999, 1187999, 1238999
Offset: 1

Views

Author

Ki Punches, Mar 28 2009

Keywords

Comments

The sequence is conjecturally infinite; note that terms ending 9999 straddle ten millennia.

Crossrefs

Cf. A060229, A158277.

Extensions

Corrected and extended by Ray Chandler and R. J. Mathar, Apr 03 2009

A161002 Least prime of three consecutive primes (p1,p2,p3) such that p2-p1 and p3-p2 are both perfect squares.

Original entry on oeis.org

9547, 12853, 22189, 22303, 27127, 29881, 32257, 40387, 42859, 46771, 46957, 47977, 57601, 60037, 60457, 71593, 72577, 73783, 77101, 84247, 88423, 89137, 90547, 93427, 97459, 97609, 97879, 112507, 115021, 118927, 126271, 127873, 131317
Offset: 1

Views

Author

Ki Punches, Jun 01 2009

Keywords

Comments

Sequence is probably infinite.
a(3859) = 11981443 is the first term in the sequence where neither of the prime gaps is 36.

Examples

			Consecutive primes (22189, 22193, 22229) have gaps (4, 36) so 22189 is in the sequence.

Links

Crossrefs

Cf. A138198.

Programs

  • Mathematica
    Transpose[Select[Partition[Prime[Range[12300]],3,1],IntegerQ[Sqrt[#[[2]]- #[[1]]]]&&IntegerQ[Sqrt[#[[3]]-#[[2]]]]&]][[1]] (* Harvey P. Dale, Dec 21 2011 *)

Extensions

Edited by Ray Chandler, Jun 08 2009

A158957 Lesser of two successive primes p1, p2, where p2-p1 (gap) includes at least one entire primeless century.

Original entry on oeis.org

1671781, 2637799, 3117299, 3933599, 4640599, 4652353, 5178193, 5518687, 5837399, 5845193, 6012899, 6084977, 6333799, 6376193, 6789793, 6958667, 7129877, 7565191, 7803491, 7826899, 8027699, 8367397, 8421251, 8905199
Offset: 1

Views

Author

Ki Punches, Apr 29 2009

Keywords

Comments

The sequence is probably infinite.

Programs

  • Mathematica
    Transpose[Select[Partition[Prime[Range[600000]],2,1],Floor[#[[2]]/100]- Floor[ #[[1]]/100]>1&]][[1]] (* Harvey P. Dale, Jul 10 2015 *)

Extensions

Corrected by Ray Chandler, Apr 30 2009

A158089 Palindromic primes that contain at least one embedded palindromic prime by removing 1 or 2 digits.

Original entry on oeis.org

101, 131, 151, 181, 191, 353, 373, 727, 757, 929, 10301, 10501, 11311, 12821, 13331, 13831, 13931, 14341, 15551, 16061, 16361, 16561, 17971, 19391, 19891, 19991, 30103, 30703, 30803, 31013, 31513, 33533, 34543, 34843, 35153, 35753, 36563
Offset: 1

Views

Author

Ki Punches, Mar 12 2009

Keywords

Comments

The only candidates for removing a single digit must be of the form 1x1 since 11 is the only palindromic prime with an even number of digits.

Crossrefs

Subsequence of A002385 (palindromic primes).

Extensions

Edited and corrected by Ray Chandler, May 24 2009

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