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 1-5 of 5 results.

A129492 Composite numbers k such that 2^k mod k is a power of 2.

Original entry on oeis.org

6, 9, 10, 12, 14, 15, 20, 21, 22, 24, 26, 28, 30, 33, 34, 38, 39, 40, 44, 46, 48, 51, 52, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 72, 74, 76, 78, 80, 82, 84, 85, 86, 87, 90, 92, 93, 94, 96, 102, 106, 111, 112, 114, 116, 118, 120, 122, 123, 124, 126, 129, 132, 133, 134, 138
Offset: 1

Views

Author

Robert G. Wilson v, Apr 17 2007

Keywords

Comments

Complement to composite numbers: 4, 8, 16, 18, 25, 27, 32, 35, 36, 42, 45, 49, 50, 54, 55, 64, 70, 75, 77, 81, 88, 91, 95, 98, 99, ....

Examples

			15 is a term since 2^15 mod 15 = 8.

Links

Crossrefs

Cf. A036236, A129493, A129494, A129495, A129496, A129497.
Contains A001567.

Programs

  • Magma
    [k:k in [2..150]| not IsPrime(k)  and  not IsZero(a)  and (PrimeDivisors(a) eq [2]) where a is 2^k mod k ]; // Marius A. Burtea, Dec 04 2019
  • Maple
    filter:= proc(n) local k;
  if isprime(n) then return false fi;
  k:= 2 &^ n mod n;
  k > 1 and k = 2^padic:-ordp(k,2)
end proc:
select(filter, [$4..1000]); # Robert Israel, Dec 03 2019
  • Mathematica
    Select[Range@ 141, IntegerQ@ Log[2, PowerMod[2, #, # ]] &]

A129494 Composite numbers k such that 4^k mod k is a power of 4 greater than 1.

Original entry on oeis.org

6, 12, 15, 20, 22, 24, 26, 28, 30, 34, 38, 40, 46, 48, 56, 58, 60, 62, 66, 69, 72, 74, 77, 80, 82, 84, 85, 86, 87, 88, 91, 93, 94, 96, 102, 104, 105, 106, 111, 117, 118, 120, 122, 123, 126, 129, 132, 134, 140, 141, 142, 144, 146, 158, 159, 166, 168, 170, 177, 178, 182
Offset: 1

Views

Author

Robert G. Wilson v, Apr 17 2007

Keywords

Comments

Complement to composite numbers: 4, 8, 9, 10, 14, 16, 18, 21, 25, 27, 32, 33, 35, 36, 39, 42, 44, 45, 49, 50, 51, 52, 54, 55, 57, ... - R. J. Mathar, May 16 2008

Examples

			22 is a term since 4^22 mod 22 = 16.

Links

Crossrefs

Cf. A036236, A129492, A129493, A129495, A129496, A129497.
Contains A122781 except for 1 and 4.

Programs

  • Magma
    [k:k in [2..200]| not IsPrime(k)  and  not IsZero(a)  and (PrimeDivisors(a) eq [2]) and  &+[j[1]*j[2]: j in Factorization(a) ] mod 4 eq 0 where a is 4^k mod k]; // Marius A. Burtea, Dec 04 2019
  • Maple
    filter:= proc(n) local k,j;
  if isprime(n) then return false fi;
  k:= 4 &^ n mod n;
  j:= padic:-ordp(k,2);
  k>1 and j::even and k = 2^j
end proc:
select(filter, [$4..1000]); # Robert Israel, Dec 03 2019
  • Mathematica
    Select[ Range@ 161, IntegerQ@ Log[4, PowerMod[4, #, # ]] &]

Extensions

Corrected and extended by R. J. Mathar, May 16 2008

A129495 Composite numbers k such that 5^k (mod k) is a power of 5 greater than 1.

Original entry on oeis.org

10, 15, 20, 26, 30, 34, 38, 40, 46, 50, 56, 58, 60, 62, 65, 74, 78, 82, 86, 94, 100, 106, 118, 120, 122, 124, 129, 130, 132, 134, 140, 141, 142, 143, 146, 150, 155, 158, 159, 166, 177, 178, 182, 183, 190, 194, 195, 200, 201, 202, 206, 213, 214, 217, 218, 219
Offset: 1

Views

Author

Robert G. Wilson v, Apr 17 2007

Keywords

Examples

			26 is a member of the sequence since 5^26 (mod 26) == 25.

Links

Crossrefs

Cf. A036236, A129492, A129493, A129494, A129496, A129497.

Programs

  • Mathematica
    Select[Range@ 225, (p = PowerMod[5, #, #]) > 1 && IntegerQ@ Log[5, p] && CompositeQ[#] &] (* corrected by Amiram Eldar, Jul 24 2021 *)

A129496 Composite numbers k such that 6^k (mod k) is a power of 6 greater than 1.

Original entry on oeis.org

10, 15, 21, 30, 35, 38, 42, 45, 46, 58, 60, 62, 70, 74, 82, 84, 86, 90, 94, 105, 106, 118, 122, 126, 132, 134, 140, 142, 146, 158, 166, 178, 180, 182, 185, 190, 194, 202, 206, 210, 214, 215, 217, 218, 219, 222, 226, 228, 231, 237, 249, 252, 254, 258, 259, 262
Offset: 1

Views

Author

Robert G. Wilson v, Apr 17 2007

Keywords

Examples

			38 is a member of the sequence since 6^38 (mod 38) == 36.

Links

Crossrefs

Cf. A036236, A129492, A129493, A129494, A129495, A129497.

Programs

  • Mathematica
    Select[Range@ 266, (p = PowerMod[6, #, #]) > 1 && IntegerQ@ Log[6, p] && CompositeQ[#] &] (* corrected by Amiram Eldar, Jul 24 2021 *)

A129497 Composite numbers k such that 7^k (mod k) is a power of 7 greater than 1.

Original entry on oeis.org

14, 21, 25, 42, 50, 56, 58, 62, 70, 74, 82, 84, 86, 94, 98, 105, 106, 112, 118, 122, 132, 133, 134, 142, 146, 147, 150, 152, 158, 166, 168, 178, 182, 194, 196, 202, 206, 210, 214, 218, 226, 231, 254, 262, 266, 274, 278, 294, 298, 301, 302, 314, 325, 326, 334
Offset: 1

Views

Author

Robert G. Wilson v, Apr 17 2007

Keywords

Examples

			58 is a member of the sequence since 7^58 (mod 58) == 49.

Links

Crossrefs

Cf. A036236, A129492, A129493, A129494, A129495, A129496.

Programs

  • Mathematica
    Select[Range@ 335, (p = PowerMod[7, #, #]) > 1 && IntegerQ@ Log[7, p] && CompositeQ[#] &] (* corrected by Amiram Eldar, Jul 24 2021 *)

Extensions

Corrected and edited by R. J. Mathar, May 16 2008
Showing 1-5 of 5 results.

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

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