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: Sebastian Petzelberger

Sebastian Petzelberger's wiki page.

Sebastian Petzelberger has authored 10 sequences.

A256842 Initial members of 5 twin primes with the smallest possible difference of 30.

Original entry on oeis.org

39713433671, 66419473031, 71525244611, 286371985811, 480612532451, 535181743301, 789972743471, 1195575264641, 1219449947921, 1256522812841, 1292207447351, 1351477467251, 1450982599271, 1460592638171, 1515361442261, 1592346154541
Offset: 1

Views

Author

Sebastian Petzelberger, Apr 21 2015

Keywords

Comments

There are 5 twin primes in a group of 39 numbers. The term 5TP39 was suggested by prime number researcher Roger Hargrave on 16-FEB-2003. It is also the lowest number of ten primes.
We only have to test primes of the form p = 2310n + 821 and p = 2310n + 1451.
Similar to A059925, but here we have additionally a twin pair of primes in the middle.

Links

Crossrefs

Cf. A059925.

A256621 Primes p such that the decimal expansion of p remains prime under three iterations of base-10 to base-2 conversion.

Original entry on oeis.org

3893257, 9023533, 11005327, 11659009, 18747809, 21855233, 25183007, 34074379, 54298687, 58562951, 60496981, 89891273, 94277683, 96602887, 102276859, 115555927, 117578429, 122191543, 125115709, 132837283, 138169991, 139442753, 168852077, 183879649, 184904831
Offset: 1

Views

Author

Sebastian Petzelberger, Apr 06 2015

Keywords

Examples

			The 3 iterations: 3893257 --> 1110110110100000001001 --> ... --> ... are prime.

Links

Crossrefs

Cf. A065720, A123266, A256622.

Programs

  • PARI
    isok(n, nb=3) = {for (k=1, nb, b = binary(n); d = eval(subst(Pol(b), x, 10)); if (! isprime(d), return (0)); n = d;); return (1);} \\ Michel Marcus, Apr 08 2015

A256622 Primes p such that the decimal expansion of p remains prime under four iterations of base-10 to base-2 conversion.

Original entry on oeis.org

9632552297, 23971039429, 32460766253, 55325366053, 75883883641, 87824771197, 91754975491, 91989527023, 97696323983
Offset: 1

Views

Author

Sebastian Petzelberger, Apr 07 2015

Keywords

Comments

Jim Fougeron and Farideh Firoozbakht independently found the first term 9632552297.
When does five iterations start?

Links

  • Carlos Rivera, Puzzle 280, The Prime Puzzles & Problems Connection.

Crossrefs

Cf. A065720, A123266, A256621.

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

Views

Author

Sebastian Petzelberger, Mar 25 2015

Keywords

Comments

Are there any remaining composites in only one other base?

Links

Crossrefs

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

Views

Author

Sebastian Petzelberger, Mar 25 2015

Keywords

Examples

			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.

Links

Crossrefs

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

Programs

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

Views

Author

Sebastian Petzelberger, Mar 25 2015

Keywords

Links

Crossrefs

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

Views

Author

Sebastian Petzelberger, Mar 25 2015

Keywords

Comments

Less remaining is not possible for even numbers.

Links

Crossrefs

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

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

Views

Author

Sebastian Petzelberger, Mar 25 2015

Keywords

Links

Crossrefs

Cf. A052026, A256350-A256356, 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

Views

Author

Sebastian Petzelberger, Mar 25 2015

Keywords

Links

Crossrefs

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

Programs

  • Maple
    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
  • Mathematica
    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 *)

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

Views

Author

Sebastian Petzelberger, Mar 25 2015

Keywords

Links

Crossrefs

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

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