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 1-8 of 8 results.

A169906 Carryless products 2*A169887, sorted and duplicates removed.

Original entry on oeis.org

2, 4, 6, 8, 20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 60, 62, 64, 66, 68, 80, 82, 84, 86, 88, 204, 206, 222, 224, 246, 248, 266, 268, 282, 284, 402, 408, 422, 426, 444, 448, 464, 468, 482, 486, 602, 608, 624, 628, 642, 646, 662, 666, 684, 688, 804, 806, 826, 828, 842, 844, 862
Offset: 1

Views

Author

David Applegate, Marc LeBrun and N. J. A. Sloane, Jul 11 2010

Keywords

Comments

Carryless doubles of the carryless primes.

Links

Crossrefs

Cf. A169887, A169907.

A169907 Carryless product 2*A169887(n).

Original entry on oeis.org

42, 46, 40, 44, 48, 82, 86, 80, 84, 88, 2, 4, 6, 8, 2, 4, 6, 8, 22, 26, 20, 24, 28, 62, 66, 60, 64, 68, 402, 408, 444, 448, 482, 486, 422, 426, 464, 468, 806, 804, 842, 844, 886, 888, 826, 828, 862, 864, 2, 6, 4, 8, 206, 204, 246, 248, 282, 284, 222, 224, 266, 268, 602, 608
Offset: 1

Views

Author

David Applegate, Marc LeBrun and N. J. A. Sloane, Jul 11 2010

Keywords

Links

Crossrefs

Cf. A169887, A169906.

A169904 Carryless squares of carryless primes (cf. A169887).

Original entry on oeis.org

405, 429, 441, 461, 489, 501, 504, 506, 509, 605, 621, 649, 669, 681, 40401, 40601, 42041, 42229, 44021, 44869, 46081, 46849, 48061, 48289, 50501, 50509, 60409, 60609, 62049, 62821, 64029, 64261, 66089, 66241, 68069, 68881
Offset: 1

Views

Author

David Applegate, Marc LeBrun and N. J. A. Sloane, Jul 11 2010

Keywords

Links

A169884 Numbers consisting of either all even digits or just 5's and 0's.

Original entry on oeis.org

0, 2, 4, 5, 6, 8, 20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 50, 55, 60, 62, 64, 66, 68, 80, 82, 84, 86, 88, 200, 202, 204, 206, 208, 220, 222, 224, 226, 228, 240, 242, 244, 246, 248, 260, 262, 264, 266, 268, 280, 282, 284, 286, 288, 400, 402, 404, 406
Offset: 1

Views

Author

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

Keywords

Comments

These are all the divisors of zero in carryless arithmetic mod 10. E.g. 5 * 44 = 0.

Links

Crossrefs

Cf. A004520, A059729, A168294, A168541, A169885, A169886, A169887.

Programs

  • Mathematica
    With[{upto=410},Select[Union[Join[Select[Range[upto],And@@EvenQ[ IntegerDigits[#]]&], FromDigits/@Tuples[{5,0},Ceiling[Log[ 10,upto]]]]],#<=upto&]] (* Harvey P. Dale, Aug 05 2011 *)
elect[Range[0,500],AllTrue[IntegerDigits[#],EvenQ]||SubsetQ[{0,5},IntegerDigits[#]]&] (* Harvey P. Dale, Aug 22 2025 *)

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.

A169984 Primes in carryless arithmetic mod 10 in which all digits except the rightmost are zero or five.

Original entry on oeis.org

51, 52, 53, 54, 56, 57, 58, 59, 551, 553, 557, 559, 5051, 5053, 5057, 5059, 5501, 5503, 5507, 5509, 50051, 50053, 50057, 50059, 55001, 55003, 55007, 55009, 55551, 55553, 55557, 55559, 500501, 500503, 500507, 500509, 505001, 505003
Offset: 1

Views

Author

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

Keywords

Comments

These are called f-type primes.

Links

Crossrefs

A169887 = A163396 union A169984.

A169903 Primitive primes in carryless arithmetic mod 10.

Original entry on oeis.org

21, 23, 25, 27, 29, 51, 56, 201, 209, 227, 229, 241, 243, 261, 263, 287, 289, 551, 2023, 2027, 2043, 2047, 2061, 2069, 2081, 2089, 2207, 2209, 2221, 2223, 2263, 2267, 2281, 2287, 2401, 2407, 2421, 2423, 2441, 2449, 2483, 2489, 2603, 2609
Offset: 1

Views

Author

David Applegate, Marc LeBrun and N. J. A. Sloane, Jul 11 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.
A prime is primitive if it is not the carryless product of a smaller prime and a unit.
A subsequence of A169887.

Links

Crossrefs

Cf. A004520, A059729, A168294, A168541, A169885, A169886, A169884, A169887.
Cf. A058943, A058945.

A169962 Number of n-digit primes in carryless arithmetic mod 10.

Original entry on oeis.org

0, 0, 28, 44, 168, 612, 2520, 10356, 44712, 195120, 868224, 3905388, 17756424, 81376140, 375603480, 1743843924, 8138028696, 38146891320, 179515196280, 847710124128, 4015470916296, 19073484584388, 90826125756552, 433488317523588, 2073205037124648
Offset: 0

Views

Author

N. J. A. Sloane, Aug 07 2010

Keywords

Links

Crossrefs

See A169887 for the actual primes.

Programs

  • Maple
    with(numtheory); f:=proc(n) local t1,d; if n <= 1 then RETURN(0); fi; t1:=0; for d from 1 to n-1 do if n-1 mod d = 0 then t1:=t1+(4/(n-1))*mobius((n-1)/d)*(2^d+5^d); fi; od: t1; end;

Formula

For formula see Maple code.
Showing 1-8 of 8 results.

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

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