A052032 -id: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.

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 *)

A038537 Primes base 10 that remain primes in eight bases b, 2<=b<=10, when the expansions are interpreted as decimal numbers.

Original entry on oeis.org

2, 3, 379081, 59771671, 146752831, 764479423, 1479830551, 3406187401, 5631714889, 7740024337, 8256310441, 8772257161, 9522879913, 10350894331, 12852250993, 14261996563, 16082349433, 16199980009, 17727606151, 18172964503, 18294784903, 19393314433, 19472325391, 20582035993

Offset: 1

Carlos Rivera

Sebastian Petzelberger, Table of n, a(n) for n = 1..54 (terms up to 10^12).
Carlos Rivera, Puzzle 24: Primes in several bases, The Prime Puzzles & Problems Connection.

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

Select[Prime[Range@ 50000], Count[PrimeQ /@ Table[FromDigits[IntegerDigits[#, i]], {i, 2, 10}], True] == 8 &] (* Michael De Vlieger, Mar 20 2015, after Harvey P. Dale at A052032 *)

a(4)-a(7) found by Jack Brennen (see link) added by Patrick De Geest, Dec 15 1999

Terms beyond a(7) from Sebastian Petzelberger, Mar 21 2015

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

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 *)

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 *)

A052031 Primes base 10 that remain primes in three bases b, 2<=b<=10, expansions interpreted as decimal numbers.

Original entry on oeis.org

11, 13, 17, 29, 31, 47, 59, 61, 83, 89, 97, 101, 109, 149, 151, 179, 181, 197, 227, 241, 251, 281, 331, 349, 353, 359, 373, 383, 419, 421, 439, 449, 457, 487, 503, 541, 547, 563, 587, 601, 617, 659, 673, 709, 727, 733, 743, 751, 773, 811, 823, 877, 953, 967

Offset: 1

Patrick De Geest, Dec 15 1999

			11 is 23_4, 13_8 and 11_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@ 165], Count[PrimeQ /@ Table[FromDigits[IntegerDigits[#, i]], {i, 2, 10}], True] == 3 &] (* Michael De Vlieger, Mar 20 2015 after Harvey P. Dale at A052032 *)

A256351 Composites in base 10 that remain composite in exactly seven bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

Original entry on oeis.org

8, 9, 15, 16, 21, 22, 25, 28, 34, 75, 87, 91, 93, 94, 106, 111, 123, 141, 143, 145, 147, 155, 172, 201, 205, 214, 217, 237, 255, 298, 304, 305, 363, 371, 376, 377, 385, 388, 395, 403, 411, 423, 428, 442, 458, 466, 471, 473, 483, 495, 501, 505, 507, 531, 533

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

Cf. A052026, A256350 - A256356.
Cf. A038537, A052027, A052028, A052029, A052030, A052031, A052032, A084482.
Cf. A052033, A236356.

f:= proc(b,x) local L,i;
L:= convert(x,base,b);
isprime(add(10^(i-1)*L[i],i=1..nops(L)))
end proc:
select(t -> not isprime(t) and nops(select(f,[$2..9],t))=2, [$1..1000]); # Robert Israel, Mar 26 2015

fQ[n_] := CompositeQ@ n && Count[ CompositeQ[ FromDigits[ IntegerDigits[n, #]] & /@ Range[2, 9]], True] == 6; Select[ Range@ 500, fQ] (* Robert G. Wilson v, Mar 26 2015 *)

A256355 Composites in base 10 that remain composite in exactly three bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

Original entry on oeis.org

11233, 42241, 98281, 131239, 161953, 315151, 358135, 606553, 692263, 785851, 1114081, 1130419, 1525777, 1906363, 3369313, 3403081, 3880873, 5616721, 6036103, 6947611, 7253191, 7516783, 7886593, 8799127, 8811223, 9108289, 9113203, 9195313, 9450361, 9600769

Offset: 1

Sebastian Petzelberger, Mar 25 2015

			11233 = 324413_5 and 324413_10 is composite; 11233 = 44515_7 and 44515_10 is composite; 11233_10 itself is composite. Interpreted in base 2, 3, 4, 6, 8, and 9 the result is prime. Hence 11233 is in this sequence.

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

Cf. A052026, A256350, A256351, A256352, A256353, A256354, A256356, A038537, A052027, A052028, A052029, A052030, A052031, A052032, A052033, A084482, A236356.

is(n)=!isprime(n) && sum(b=2,9,isprime(fromdigits(digits(n,b))))==6 \\ Charles R Greathouse IV, Apr 23 2015

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.

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A038537 Primes base 10 that remain primes in eight bases b, 2<=b<=10, when the expansions are interpreted as decimal numbers.

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

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

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

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PARI

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

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A052031 Primes base 10 that remain primes in three bases b, 2<=b<=10, expansions interpreted as decimal numbers.

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A256351 Composites in base 10 that remain composite in exactly seven bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

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Maple

Mathematica

A256355 Composites in base 10 that remain composite in exactly three bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

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Keywords

Examples

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PARI