A256350 -id:A256350 - cp's OEIS frontend

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

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.

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 *)

A256352 Composites in base 10 that remain composite in exactly six bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

Original entry on oeis.org

10, 33, 39, 133, 183, 185, 203, 235, 291, 295, 303, 325, 343, 381, 391, 451, 475, 517, 535, 539, 561, 583, 655, 703, 723, 753, 775, 791, 799, 841, 867, 889, 895, 943, 1003, 1023, 1083, 1099, 1121, 1159, 1165, 1173, 1186, 1198, 1207, 1219, 1263, 1333, 1366

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, A038537, A052027-A052033, A084482, A236356.

A256353 Composites in base 10 that remain composite in exactly five bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

Original entry on oeis.org

55, 169, 247, 253, 323, 493, 529, 556, 671, 1027, 1111, 1243, 1261, 1339, 1375, 1711, 1751, 1803, 2185, 2413, 2431, 2881, 3193, 4381, 4417, 4843, 5029, 5203, 5251, 6631, 7093, 7999, 8515, 8653, 9271, 9307, 9481, 9523, 9593, 9727, 9745, 9937, 9955, 10393, 10555

Offset: 1

Sebastian Petzelberger, Mar 25 2015

Less remaining is not possible for even numbers.

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, A038537, A052027-A052033, A084482, A236356.

A256354 Composites in base 10 that remain composite in exactly four bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

Original entry on oeis.org

115, 2563, 3523, 5071, 9193, 10873, 12223, 12811, 13231, 15775, 19111, 20203, 23089, 25831, 27007, 28171, 34189, 39859, 40033, 43361, 55033, 57871, 58813, 74371, 84253, 89377, 93043, 95833, 101683, 117001, 125359, 126673, 128953, 131029, 134527, 137467, 138193

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, A038537, A052027-A052033, A084482, A236356.

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

A256356 Composites in base 10 that remain composite in exactly two 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

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A256352 Composites in base 10 that remain composite in exactly six bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

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A256353 Composites in base 10 that remain composite in exactly five bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

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A256354 Composites in base 10 that remain composite in exactly four bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

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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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PARI