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 1-6 of 6 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.

A169885 Cubes (n * n * n) in carryless arithmetic mod 10.

Original entry on oeis.org

0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 1000, 1331, 1628, 1977, 1284, 1555, 1886, 1173, 1422, 1739, 8000, 8261, 8448, 8647, 8864, 8005, 8266, 8443, 8642, 8869, 7000, 7791, 7468, 7117, 7844, 7555, 7246, 7913, 7662, 7399, 4000, 4821, 4688, 4487, 4224, 4005, 4826, 4683
Offset: 0

Views

Author

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

Keywords

Links

Crossrefs

Cf. A004520, A059729, A168294, A168541, A169884, A169886.

Programs

  • PARI
    a(n) = fromdigits(Vec(Pol(digits(n))^3)%10); \\ Seiichi Manyama, Mar 09 2023

A169886 Fourth powers (n * n * n * n) in carryless arithmetic mod 10.

Original entry on oeis.org

0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 10000, 14641, 18426, 12481, 16666, 10005, 14646, 18421, 12486, 16661, 60000, 62481, 64646, 66661, 68426, 60005, 62486, 64641, 66666, 68421, 10000, 18421, 16666, 14641, 12486, 10005, 18426, 16661, 14646, 12481, 60000, 66661, 62486
Offset: 0

Views

Author

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

Keywords

Links

Crossrefs

Cf. A004520, A059729, A168294, A168541, A169884, A169885.

Programs

  • PARI
    a(n) = fromdigits(Vec(Pol(digits(n))^4)%10); \\ Seiichi Manyama, Mar 09 2023

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 *)

A168541 Numbers consisting of either 2's and 0's or 5's and 0's.

Original entry on oeis.org

2, 5, 20, 50, 200, 202, 220, 500, 505, 550, 2000, 2002, 2020, 2022, 2200, 2202, 2220, 5000, 5005, 5050, 5055, 5500, 5505, 5550, 20000, 20002, 20020, 20022, 20200, 20202, 20220, 20222, 22000, 22002, 22020, 22022, 22200, 22202, 22220, 50000, 50005
Offset: 1

Views

Author

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

Keywords

Comments

A subset of the divisors of zero in carryless arithmetic mod 10, e.g., 5 * 44 = 0.

Links

Crossrefs

Cf. A004520, A059729, A168294, A169884.

Programs

  • Mathematica
    lst = {2, 5}; k = 1; While[k < 10^5, id = Union@ IntegerDigits@k; len = Length@ id; If[ len == 2 && id == {0, 2} || id == {0, 5}, AppendTo[lst, k]]; k++ ]; lst (* Robert G. Wilson v, Jul 12 2010 *)
Join[{2,5},Sort[Flatten[Table[Select[FromDigits/@Tuples[{k,0},6],DigitCount[ #,10,0]>0 && DigitCount[#,10,k]>0&],{k,{2,5}}]]]] (* Harvey P. Dale, Jul 03 2020 *)

Extensions

More terms from Robert G. Wilson v, Jul 12 2010

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.
Showing 1-6 of 6 results.

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

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