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.

A225506 -2-Knödel numbers.

Original entry on oeis.org

4, 6, 8, 10, 12, 24, 28, 30, 70, 88, 130, 238, 510, 754, 868, 910, 1330, 2068, 2590, 2728, 3304, 4002, 5110, 5406, 8554, 8710, 12958, 15748, 18430, 20878, 21238, 23902, 24178, 32422, 39928, 46870, 49210, 53590, 55678, 57358, 62248, 67858, 70414, 79378, 88198, 95038, 95758, 95788, 102238, 114478
Offset: 1

Views

Author

Paolo P. Lava, May 09 2013

Keywords

Comments

Extension of k-Knödel numbers to k negative, in this case equal to -2. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+2) = 1 mod n.
All terms are even numbers.

Links

Crossrefs

Cf. A208728.
Cf. A225507, A225508, A225509, A225510, A225511, A225512, A225513, A225514.

Programs

  • Maple
    with(numtheory); ListA225506:=proc(q,k) local a,n,ok;
for n from 2 to q do if not isprime(n) then ok:=1; for a from 1 to n do
if gcd(a,n)=1 then if (a^(n-k)-1) mod n<>0 then ok:=0; break; fi; fi;
od; if ok=1 then print(n); fi; fi; od; end: ListA225506(10^6,-2);
  • Mathematica
    Select[Range[10000], CompositeQ[#] && Divisible[# + 2, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)
  • PARI
    is(n) = forprime(p=3, n, if (n%p != 0 && Mod(p,n)^(n+2) != 1, return(0))); 1;
seq(N) = {
  my(a=vector(N), k=0, n=4);
  while(k < N, if(is(n), a[k++] = n); n += 2);
  a;
};
seq(50) \\ Gheorghe Coserea, Dec 23 2018

Extensions

More terms from Gheorghe Coserea, Dec 23 2018

A225507 -3-Knödel numbers.

Original entry on oeis.org

9, 21, 45, 63, 105, 117, 273, 285, 585, 627, 765, 1365, 1449, 1677, 3705, 3885, 4221, 4485, 4797, 7137, 7565, 8109, 10197, 10545, 11445, 13065, 14637, 16965, 19437, 20805, 26061, 27645, 30573, 31317, 33705, 35853, 38805, 39897, 40887, 41181, 48633, 50505, 57057
Offset: 1

Views

Author

Paolo P. Lava, May 09 2013

Keywords

Comments

Extension of k-Knödel numbers to k negative, in this case equal to -3. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+3) = 1 mod n.

Links

Crossrefs

Cf. A208728.
Cf. A225506, A225508, A225509, A225510, A225511, A225512, A225513, A225514.

Programs

  • Maple
    with(numtheory); ListA225507:=proc(q,k) local a,n,ok;
for n from 2 to q do if not isprime(n) then ok:=1; for a from 1 to n do
if gcd(a,n)=1 then if (a^(n-k)-1) mod n<>0 then ok:=0; break; fi; fi;
od; if ok=1 then print(n); fi; fi; od; end: ListA225507(10^6,-3);
  • Mathematica
    Select[Range[10000], CompositeQ[#] && Divisible[# + 3, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)

Extensions

Incorrect comment deleted by Joseph DeVincentis, Dec 04 2015
More terms from Amiram Eldar, Mar 28 2019

A225509 -5-Knödel numbers.

Original entry on oeis.org

15, 55, 75, 91, 175, 247, 275, 715, 775, 1275, 1435, 2275, 2635, 3075, 3355, 4615, 6355, 6475, 7975, 8827, 9139, 10075, 10675, 11275, 11935, 13515, 14555, 21775, 26455, 28975, 30415, 31675, 32395, 43615, 46075, 47275, 52195, 59755, 64255, 77275, 78403, 81055
Offset: 1

Views

Author

Paolo P. Lava, May 09 2013

Keywords

Comments

Extension of k-Knödel numbers to k negative, in this case equal to -5. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+5) = 1 mod n.

Links

Crossrefs

Cf. A208728.
Cf. A225506, A225507, A225508, A225510, A225511, A225512, A225513, A225514,

Programs

  • Maple
    with(numtheory); ListA225509:=proc(q,k) local a,n,ok;
for n from 2 to q do if not isprime(n) then ok:=1; for a from 1 to n do
if gcd(a,n)=1 then if (a^(n-k)-1) mod n<>0 then ok:=0; break; fi; fi;
od; if ok=1 then print(n); fi; fi; od; end: ListA225509(10^6,-5);
  • Mathematica
    Select[Range[10000], CompositeQ[#] && Divisible[# + 5, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)

Extensions

More terms from Amiram Eldar, Mar 28 2019

A225510 -6-Knödel numbers.

Original entry on oeis.org

4, 6, 8, 10, 12, 18, 24, 30, 36, 42, 44, 72, 78, 84, 90, 126, 168, 170, 210, 228, 234, 252, 264, 390, 504, 546, 570, 630, 714, 744, 924, 1110, 1170, 1254, 1530, 1548, 1596, 1638, 2262, 2574, 2604, 2730, 2898, 3354, 3978, 3990, 4674, 5544, 5688, 6204, 7254, 7410
Offset: 1

Views

Author

Paolo P. Lava, May 09 2013

Keywords

Comments

Extension of k-Knodel numbers to k negative, in this case equal to -6. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+6) = 1 mod n.

Links

Crossrefs

Cf. A208728.
Cf. A225506, A225507, A225508, A225509, A225511, A225512, A225513, A225514.

Programs

  • Maple
    with(numtheory); ListA225510:=proc(q,k) local a,n,ok;
for n from 2 to q do if not isprime(n) then ok:=1; for a from 1 to n do
if gcd(a,n)=1 then if (a^(n-k)-1) mod n<>0 then ok:=0; break; fi; fi;
od; if ok=1 then print(n); fi; fi; od; end: ListA225510(10^6,-6);
  • Mathematica
    Select[Range[10000], CompositeQ[#] && Divisible[# + 6, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)

A225511 -7-Knödel numbers.

Original entry on oeis.org

33, 65, 245, 345, 1353, 1421, 1505, 2405, 3185, 4433, 4745, 6293, 6923, 7733, 8729, 9065, 9443, 9785, 15113, 16113, 18473, 19565, 21593, 30485, 30705, 32513, 35705, 42833, 45353, 50141, 55685, 57017, 64505, 66521, 67065, 73073, 79553, 80093, 83657, 91553, 96473
Offset: 1

Views

Author

Paolo P. Lava, May 09 2013

Keywords

Comments

Extension of k-Knodel numbers to k negative, in this case equal to -7. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+7) = 1 mod n.

Links

Crossrefs

Cf. A208728.
Cf. A225506, A225507, A225508, A225509, A225510, A225512, A225513, A225514.

Programs

  • Maple
    with(numtheory); ListA225511:=proc(q,k) local a,n,ok;
for n from 2 to q do if not isprime(n) then ok:=1; for a from 1 to n do
if gcd(a,n)=1 then if (a^(n-k)-1) mod n<>0 then ok:=0; break; fi; fi;
od; if ok=1 then print(n); fi; fi; od; end: ListA225511(10^6,-7);
  • Mathematica
    Select[Range[10000], CompositeQ[#] && Divisible[# + 7, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)

Extensions

More terms from Amiram Eldar, Mar 28 2019

A225512 -8-Knödel numbers.

Original entry on oeis.org

4, 6, 8, 12, 16, 20, 22, 24, 28, 32, 40, 48, 52, 60, 80, 96, 112, 120, 132, 136, 160, 208, 240, 280, 322, 352, 364, 408, 480, 520, 532, 580, 680, 682, 952, 1036, 1120, 1312, 1392, 1456, 1612, 1768, 1840, 2040, 2080, 2332, 2584, 3016, 3172, 3268, 3472, 3640
Offset: 1

Views

Author

Paolo P. Lava, May 09 2013

Keywords

Comments

Extension of k-Knodel numbers to k negative, in this case equal to -8. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+8) = 1 mod n.

Links

Crossrefs

Cf. A208728.
Cf. A225506, A225507, A225508, A225509, A225510, A225511, A225513, A225514.

Programs

  • Maple
    with(numtheory); ListA225512:=proc(q,k) local a,n,ok;
for n from 2 to q do if not isprime(n) then ok:=1; for a from 1 to n do
if gcd(a,n)=1 then if (a^(n-k)-1) mod n<>0 then ok:=0; break; fi; fi;
od; if ok=1 then print(n); fi; fi; od; end: ListA225512(10^6,-8);
  • Mathematica
    Select[Range[10000], CompositeQ[#] && Divisible[# + 8, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)
  • PARI
    is(n) = if (bigomega(n)>1, for (a=2, n-1, if (gcd(n,a)==1 && Mod(a,n)^(n+8)!=1, return (0))); return (1), return (0)) \\ Rémy Sigrist, Mar 03 2019

Extensions

More terms from Rémy Sigrist, Mar 03 2019

A225513 -9-Knödel numbers.

Original entry on oeis.org

9, 15, 21, 27, 39, 63, 135, 171, 189, 195, 231, 315, 351, 513, 651, 663, 819, 855, 999, 1197, 1755, 1881, 2223, 2295, 2331, 3111, 3591, 4095, 4347, 4599, 4995, 5031, 5301, 6327, 7161, 9471, 9855, 10431, 10791, 11115, 11655, 12663, 12987, 13455, 14091, 14391
Offset: 1

Views

Author

Paolo P. Lava, May 09 2013

Keywords

Comments

Extension of k-Knodel numbers to k negative, in this case equal to -9. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+9) = 1 mod n.

Links

Crossrefs

Cf. A208728.
Cf. A225506, A225507, A225508, A225509, A225510, A225511, A225512, A225514.

Programs

  • Maple
    with(numtheory); ListA225513:=proc(q,k) local a,n,ok;
for n from 2 to q do if not isprime(n) then ok:=1; for a from 1 to n do
if gcd(a,n)=1 then if (a^(n-k)-1) mod n<>0 then ok:=0; break; fi; fi;
od; if ok=1 then print(n); fi; fi; od; end: ListA225513(10^6,-9);
  • Mathematica
    Select[Range[10000], CompositeQ[#] && Divisible[# + 9, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)

Extensions

More terms from Amiram Eldar, Mar 28 2019

A225514 -10-Knödel numbers.

Original entry on oeis.org

4, 6, 8, 10, 12, 14, 24, 26, 30, 50, 56, 102, 110, 150, 152, 182, 276, 330, 350, 494, 550, 650, 770, 962, 1190, 1230, 1430, 1550, 1650, 2550, 2870, 3050, 3410, 3752, 3770, 4510, 4550, 5270, 6150, 6650, 6710, 9230, 9350, 10010, 10850, 11526, 12710, 12950, 15950
Offset: 1

Views

Author

Paolo P. Lava, May 09 2013

Keywords

Comments

Extension of k-Knödel numbers to k negative, in this case equal to -10. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+10) = 1 mod n.

Links

Crossrefs

Cf. A208728.
Cf. A225506, A225507, A225508, A225509, A225510, A225511, A225512, A225513.

Programs

  • Maple
    with(numtheory); ListA225514:=proc(q,k) local a,n,ok;
for n from 2 to q do if not isprime(n) then ok:=1; for a from 1 to n do
if gcd(a,n)=1 then if (a^(n-k)-1) mod n<>0 then ok:=0; break; fi; fi;
od; if ok=1 then print(n); fi; fi; od; end: ListA225514(10^6,-10);
  • Mathematica
    Select[Range[10000], CompositeQ[#] && Divisible[# + 10, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)

Extensions

More terms from Amiram Eldar, Mar 28 2019
Showing 1-8 of 8 results.

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