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.

Showing 1-4 of 4 results.

A169887 Primes in carryless arithmetic mod 10.

Original entry on oeis.org

21, 23, 25, 27, 29, 41, 43, 45, 47, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 63, 65, 67, 69, 81, 83, 85, 87, 89, 201, 209, 227, 229, 241, 243, 261, 263, 287, 289, 403, 407, 421, 427, 443, 449, 463, 469, 481, 487, 551, 553, 557, 559, 603, 607, 623, 629, 641, 647, 661, 667, 683, 689, 801, 809, 821, 823, 847, 849, 867, 869, 881, 883
Offset: 1

Views

Author

David Applegate, Marc LeBrun and N. J. A. Sloane, Jul 06 2010

Keywords

Comments

Define the units in carryless arithmetic mod 10 to be the numbers 1, 3, 7 and 9 (these divide any number). A prime is a number N, not a unit, whose only factorizations are of the form N = u * M, where u is a unit.
There are two types: e-type primes (A163396) and f-type (A169984).

Examples

			Examples of nonprimes: 2 = 2*51, 4 = 2*2, 10 = 52*85, 11 = 57*83, 101 = 13*17, 102 = 58 * 254 = 502 * 801, 103 = 53 * 251 = 507 * 809, 107 = 53 * 259 = 507 * 801, 108 = 58 * 256 = 502 * 809, 111 = 227 * 553.

Links

Crossrefs

A169887 = A163396 union A169984.
Cf. A004520, A059729, A168294, A168541, A169885, A169886, A169884, A169903 (primitive primes).
Cf. A169962.

A163396 Primes in carryless arithmetic mod 10 in which all digits except the rightmost are even.

Original entry on oeis.org

21, 23, 25, 27, 29, 41, 43, 45, 47, 49, 61, 63, 65, 67, 69, 81, 83, 85, 87, 89, 201, 209, 227, 229, 241, 243, 261, 263, 287, 289, 403, 407, 421, 427, 443, 449, 463, 469, 481, 487, 603, 607, 623, 629, 641, 647, 661, 667, 683, 689, 801, 809, 821
Offset: 1

Views

Author

David Applegate, Marc LeBrun and N. J. A. Sloane, Aug 24 2010

Keywords

Comments

These are called e-type primes.

Links

Crossrefs

A169887 = A163396 union A169984.

A143712 Numbers with at least two digits in which all digits except the rightmost are even and the rightmost is odd.

Original entry on oeis.org

21, 23, 25, 27, 29, 41, 43, 45, 47, 49, 61, 63, 65, 67, 69, 81, 83, 85, 87, 89, 201, 203, 205, 207, 209, 221, 223, 225, 227, 229, 241, 243, 245, 247, 249, 261, 263, 265, 267, 269, 281, 283, 285, 287, 289, 401, 403, 405, 407, 409, 421, 423, 425, 427, 429, 441, 443, 445, 447
Offset: 1

Views

Author

David Applegate, Marc LeBrun and N. J. A. Sloane, Aug 24 2010

Keywords

Comments

These are called e-type numbers, cf. A163396.

Links

Crossrefs

Cf. A144162, A163396, A169984.

Programs

  • Mathematica
    Select[Range[21, 500], (id = IntegerDigits[#1]; And @@ EvenQ /@ Most[id] && OddQ[Last[id]]) & ] (* Jean-François Alcover, May 23 2013 *)
eodQ[n_]:=Module[{td=TakeDrop[IntegerDigits[n],-1]},OddQ[td[[1,1]]]&&AllTrue[ td[[2]],EvenQ]]; Select[Range[10,500],eodQ] (* Harvey P. Dale, Aug 06 2022 *)

A144162 Numbers with at least two digits in which all digits except the rightmost are 0 or 5 and the rightmost is neither 0 nor 5.

Original entry on oeis.org

51, 52, 53, 54, 56, 57, 58, 59, 501, 502, 503, 504, 506, 507, 508, 509, 551, 552, 553, 554, 556, 557, 558, 559, 5001, 5002, 5003, 5004, 5006, 5007, 5008, 5009, 5051, 5052, 5053, 5054, 5056, 5057, 5058, 5059, 5501, 5502, 5503, 5504, 5506, 5507, 5508, 5509, 5551
Offset: 1

Views

Author

David Applegate, Marc LeBrun and N. J. A. Sloane, Aug 24 2010

Keywords

Comments

These are called f-type numbers, cf. A163396.

Links

Crossrefs

Cf. A143712, A163396, A169984.

Programs

  • Mathematica
    Flatten[Table[10#+r,{r,{1,2,3,4,6,7,8,9}}]&/@FromDigits/@(Join[{5},#]&/@ Flatten[ Table[Tuples[{0,5},f],{f,0,3}],1])] (* Harvey P. Dale, Oct 18 2020 *)
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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