A038537 -id:A038537 - cp's OEIS frontend

A052033 Primes base 10 that are never primes in any smaller base b, 2<=b<10, expansions interpreted as decimal numbers.

263, 269, 347, 397, 431, 461, 479, 499, 569, 599, 607, 677, 683, 719, 769, 797, 821, 929, 941, 1019, 1031, 1049, 1051, 1061, 1069, 1103, 1181, 1223, 1229, 1237, 1297, 1307, 1367, 1399, 1409, 1439, 1453, 1487, 1489, 1523, 1553, 1559, 1571, 1619, 1637

Offset: 1

Patrick De Geest, Dec 15 1999

Sebastian Petzelberger, Table of n, a(n) for n = 1..10000
C. Rivera, PP&P Puzzle 24: Primes in several bases

Cf. A038537, A052026-A052033, A236174, A236437, A235354, A235377.

Select[Prime[Range@ 265], Count[PrimeQ /@ Table[FromDigits[IntegerDigits[#, i]], {i, 2, 9}], True] == 0 &] (* Michael De Vlieger, Mar 20 2015 after Harvey P. Dale at A052032 *)

A052026 Composites base 10 that remain composite in all bases b, 2<=b<=10, expansions interpreted as decimal numbers.

Original entry on oeis.org

14, 18, 20, 24, 30, 32, 36, 40, 42, 44, 51, 54, 60, 62, 69, 70, 72, 74, 76, 78, 80, 86, 90, 92, 96, 98, 99, 100, 102, 104, 108, 110, 112, 114, 120, 124, 125, 126, 128, 129, 130, 132, 135, 140, 144, 146, 148, 150, 152, 156, 158, 159, 160, 162, 164, 168, 170, 174

Offset: 1

Patrick De Geest, Dec 15 1999

Sebastian Petzelberger, Table of n, a(n) for n = 1..10000
Carlos Rivera, Puzzle 24. Primes in several bases, The Prime Puzzles & Problems Connection.

Cf. A038537, A052027-A052033, A084482, A236356

Select[Range@ 174, AllTrue[Table[FromDigits[IntegerDigits[#, i]], {i, 2, 10}], CompositeQ] &] (* Michael De Vlieger, Mar 24 2015, version 10 *)

A084482 Primes base 10 that remain primes in all nine bases b, 2<=b<=10, when the expansions are interpreted as decimal numbers.

Original entry on oeis.org

50006393431, 727533146383, 2250332130313, 2651541199513, 4437592255351, 4877749016143, 6777899690983, 7417899095713, 7431376081543, 7766799025303, 9078654198463, 10712216924641, 12244626455491, 13562282568103, 14180813918071, 14833027106593, 19479075240913, 19971686697103, 23196986067193, 34431442237963, 36429184518721, 49198998504223

Offset: 1

Jack Brennen, Jun 29 2003

a(1) found by Jack Brennen on Jul 13 2001; remaining terms computed by Jack Brennen, Nov 15 2001.

The number must end with 1, 3, 7, or 9 in each base from 2 to 10; thus must be congruent to: 1 (mod 2), 1 (mod 3), 1 or 3 (mod 4), 1 or 3 (mod 5), 1 (mod 6), 1 or 3 (mod 7), 1 or 3 or 7 (mod 8), 1 or 7 (mod 9), 1 or 3 or 7 or 9 (mod 10).

Carlos Rivera, PP and P Puzzle 24: Primes in several bases

Cf. A052026, A038537, A052027-A052033, A084482, A236356.

isok(n) = sum(b=2, 10, isprime(subst(Pol(digits(n, b)), x, 10))) == 9; \\ Michel Marcus, Mar 22 2015

Thanks to David W. Wilson for proposing the sequence and W. Edwin Clark for verifying the terms using Maple's command isprime.

A052027 Primes in base 10 that remain primes in seven bases b, 2<=b<=10, expansions interpreted as decimal numbers.

Original entry on oeis.org

5, 9241, 17791, 330289, 391231, 1005481, 1210483, 2378143, 2469241, 2779939, 2840041, 6817501, 8320831, 9865711, 10871407, 11087191, 12259603, 13645393, 15665833, 16707883, 17694463, 25751863, 27794287, 31488481

Offset: 1

Patrick De Geest, Dec 15 1999

Sebastian Petzelberger, Table of n, a(n) for n = 1..1000
Carlos Rivera, PP&P Puzzle 24: Primes in several bases

Cf. A052026, A038537, A052027-A052033, A084482, A236356.

Select[Prime[Range@ 100000], Count[PrimeQ /@ Table[FromDigits[IntegerDigits[#, i]], {i, 2, 10}], True] == 7 &] (* Michael De Vlieger, Mar 21 2015, after Harvey P. Dale at A052032 *)

Missing terms 2378143 and 2469241 added by Sebastian Petzelberger, Mar 21 2015

A052032 Primes base 10 that remain prime in one (and only one) other base b, 2<=b<10, expansions interpreted as decimal numbers.

Original entry on oeis.org

41, 53, 73, 107, 113, 131, 137, 139, 167, 173, 223, 233, 239, 257, 271, 293, 317, 389, 401, 467, 491, 509, 521, 557, 593, 641, 661, 691, 701, 739, 761, 809, 827, 829, 839, 853, 859, 863, 881, 887, 911, 937, 971, 977, 991, 1013, 1063, 1109, 1129, 1151, 1153

Offset: 1

Patrick De Geest, Dec 15 1999

Sebastian Petzelberger, Table of n, a(n) for n = 1..10000 [This replaces an earlier b-file computed by Harvey P. Dale]
C. Rivera, PP&P Puzzle 24: Primes in several bases

Cf. A038537, A052026-A052033.

Select[Prime[Range[200]],Count[PrimeQ/@Table[FromDigits[ IntegerDigits[ #,i]],{i,2,9}],True]==1&] (* Harvey P. Dale, Oct 13 2012 *)

Definition clarified by Harvey P. Dale, Oct 13 2012

A052028 Primes base 10 that remain primes in six bases b, 2<=b<=10, expansions interpreted as decimal numbers.

Original entry on oeis.org

157, 523, 1249, 1483, 1753, 4051, 9187, 10531, 22921, 25981, 29599, 35899, 51031, 57751, 67579, 79939, 98323, 103561, 110581, 148471, 150193, 150343, 249703, 259183, 277063, 278623, 331081, 335833, 353401, 391903, 424819, 435553, 504547

Offset: 1

Patrick De Geest, Dec 15 1999

Sebastian Petzelberger, Table of n, a(n) for n = 1..10000
C. Rivera, PP&P Puzzle 24: Primes in several bases

Cf. A038537, A052026-A052033.

Select[Prime[Range@ 42000], Count[PrimeQ /@ Table[FromDigits[IntegerDigits[#, i]], {i, 2, 10}], True] == 6 &] (* Michael De Vlieger, Mar 20 2015, after Harvey P. Dale at A052032 *)

A256350 Composites in base 10 that remain composite in exactly eight bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

Original entry on oeis.org

4, 6, 12, 26, 27, 35, 38, 45, 46, 48, 49, 50, 52, 56, 57, 58, 63, 64, 65, 66, 68, 77, 81, 82, 84, 85, 88, 95, 105, 116, 117, 118, 119, 121, 122, 134, 136, 138, 142, 153, 154, 161, 165, 166, 171, 175, 176, 187, 188, 190, 192, 195, 207, 208, 218, 219, 220, 225

Offset: 1

Sebastian Petzelberger, Mar 25 2015

Sebastian Petzelberger, Table of n, a(n) for n = 1..10000
Carlos Rivera, PP&P Puzzle 24: Primes in several bases, The Prime Puzzles & Problems Connection.

Cf. A052026, A256350-A256356, A038537, A052027-A052033, A084482, A236356.

A256356 Composites in base 10 that remain composite in exactly two bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

Original entry on oeis.org

33247243, 64037779, 104865433, 130237003, 238561081, 550677781, 947051353, 1013991553, 1246382791, 1343122201, 1607697631, 1609062751, 1632753601, 1788658063, 2203645111, 2364166213, 2393866411, 2480419783, 2518589671, 2544177511, 2668538575, 3029334883

Offset: 1

Sebastian Petzelberger, Mar 25 2015

Are there any remaining composites in only one other base?

Sebastian Petzelberger, Table of n, a(n) for n = 1..150
Carlos Rivera, PP&P Puzzle 24: Primes in several bases

Cf. A052026, A256350, A256351, A256352, A256353, A256354, A256355.

Cf. A038537, A052027-A052033, A084482, A236356.

A052029 Primes base 10 that remain primes in five bases b, 2<=b<=10, expansions interpreted as decimal numbers.

Original entry on oeis.org

7, 43, 71, 163, 199, 283, 307, 367, 463, 571, 757, 1033, 1163, 1627, 1873, 2683, 3041, 3691, 3967, 4483, 4651, 4729, 4951, 4973, 5407, 6073, 6961, 7351, 7537, 8053, 8599, 9103, 9817, 10321, 10831, 11251, 11383, 11743, 12433, 12853, 13219, 14419, 14479

Offset: 1

Patrick De Geest, Dec 15 1999

Sebastian Petzelberger, Table of n, a(n) for n = 1..10000
C. Rivera, PP&P Puzzle 24: Primes in several bases

Cf. A038537, A052026-A052033.

Select[Prime[Range@ 1800], Count[PrimeQ /@ Table[FromDigits[IntegerDigits[#, i]], {i, 2, 10}], True] == 5 &] (* Michael De Vlieger, Mar 20 2015, after Harvey P. Dale at A052032 *)

lista(nn, nb=5) = {forprime(p=2, nn, if (sum(b=2, 10, isprime(subst(Pol(digits(p, b)), x, 10))) == nb, print1(p, ", ")););} \\ Michel Marcus, Mar 21 2015

A052030 Primes base 10 that remain primes in four bases b, 2<=b<=10, expansions interpreted as decimal numbers.

Original entry on oeis.org

19, 23, 37, 67, 79, 103, 127, 191, 193, 211, 229, 277, 311, 313, 337, 379, 409, 433, 443, 577, 613, 619, 631, 643, 647, 653, 787, 857, 883, 907, 919, 947, 997, 1021, 1039, 1087, 1097, 1123, 1171, 1279, 1423, 1429, 1447, 1459, 1471, 1567, 1597, 1669, 1693

Offset: 1

Patrick De Geest, Dec 15 1999

			19 is 103_4, 31_6, 23_8 and 19_10.

Sebastian Petzelberger, Table of n, a(n) for n = 1..10000
C. Rivera, PP&P Puzzle 24: Primes in several bases

Cf. A038537, A052026-A052033.

Select[Prime[Range@ 265], Count[PrimeQ /@ Table[FromDigits[IntegerDigits[#, i]], {i, 2, 10}], True] == 4 &] (* Michael De Vlieger, Mar 20 2015 after Harvey P. Dale at A052032 *)

cp's OEIS Frontend

A052033 Primes base 10 that are never primes in any smaller base b, 2<=b<10, expansions interpreted as decimal numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A052026 Composites base 10 that remain composite in all bases b, 2<=b<=10, expansions interpreted as decimal numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A084482 Primes base 10 that remain primes in all nine bases b, 2<=b<=10, when the expansions are interpreted as decimal numbers.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Extensions

A052027 Primes in base 10 that remain primes in seven bases b, 2<=b<=10, expansions interpreted as decimal numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

A052032 Primes base 10 that remain prime in one (and only one) other base b, 2<=b<10, expansions interpreted as decimal numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

A052028 Primes base 10 that remain primes in six bases b, 2<=b<=10, expansions interpreted as decimal numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A256350 Composites in base 10 that remain composite in exactly eight bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

Views

Author

Keywords

Links

Crossrefs

A256356 Composites in base 10 that remain composite in exactly two bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

Views

Author

Keywords

Comments

Links

Crossrefs

A052029 Primes base 10 that remain primes in five bases b, 2<=b<=10, expansions interpreted as decimal numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

A052030 Primes base 10 that remain primes in four bases b, 2<=b<=10, expansions interpreted as decimal numbers.

Views

Author

Keywords

Examples