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 1-3 of 3 results.

A125866 Odd numbers k such that cos(2*Pi/k) is an algebraic number of a 3-smooth degree, but not 2-smooth.

Original entry on oeis.org

7, 9, 13, 19, 21, 27, 35, 37, 39, 45, 57, 63, 65, 73, 81, 91, 95, 97, 105, 109, 111, 117, 119, 133, 135, 153, 163, 171, 185, 189, 193, 195, 219, 221, 243, 247, 259, 273, 285, 291, 315, 323, 327, 333, 351, 357, 365, 399, 405, 433, 455, 459, 481, 485, 487, 489
Offset: 1

Views

Author

Artur Jasinski, Dec 13 2006

Keywords

Comments

Odd terms of A051913.
This sequence is infinite (unlike A004729), because it contains any A058383(n) times any power of 3.
A regular polygon of a(n) sides can be constructed if one also has an angle trisector.

Links

Crossrefs

Cf. A004729, A051913, A058383, A125867-A125878.

Programs

  • Maple
    filter:= proc(n) local r,a,b;
  r:= numtheory:-phi(n);
  a:= padic:-ordp(r,2);
  b:= padic:-ordp(r,3);
  if b = 0 then return false fi;
  r = 2^a*3^b;
end proc:
select(filter, [seq(i,i=3..1000,2)]); # Robert Israel, May 11 2020
  • Mathematica
    Do[If[Take[FactorInteger[EulerPhi[2n+1]][[ -1]], 1]=={3},Print[2n+1]],{n,1,10000}]

Extensions

Edited by Don Reble, Apr 24 2007

A061599 Primes p such that the greatest prime divisor of p-1 is 5.

Original entry on oeis.org

11, 31, 41, 61, 101, 151, 181, 241, 251, 271, 401, 541, 601, 641, 751, 811, 1201, 1601, 1621, 1801, 2161, 2251, 3001, 4001, 4051, 4801, 4861, 6481, 7681, 8101, 8641, 9001, 9601, 9721, 11251, 14401, 15361, 16001, 19441, 21601, 21871, 22501, 23041, 24001
Offset: 1

Views

Author

Labos Elemer, Jun 13 2001

Keywords

Comments

Prime numbers n for which cos(2Pi/n) is an algebraic number of 5th degree. - Artur Jasinski, Dec 13 2006
The least significant digit of each term is one. - Harvey P. Dale, Jul 07 2024

Links

Crossrefs

The 3rd in a family of sequences after A019434(=Fermat-primes) and A058383.
Cf. A019434, A058383, A023503, A034694, A006530, A006093, A035095, A000040.
Cf. A004729, A058383, A125867-A125875, A024899.

Programs

  • Mathematica
    Do[If[Take[FactorInteger[EulerPhi[2n + 1]][[ -1]],1] == {5} && PrimeQ[2n + 1], Print[2n + 1]], {n, 1, 10000}] (* Artur Jasinski, Dec 13 2006 *)
Select[Prime[Range[3000]],Max[FactorInteger[#-1][[;;,1]]]==5&] (* Harvey P. Dale, Jul 07 2024 *)
  • PARI
    { default(primelimit, 167772161); n=0; forprime (p=3, 167772161, f=factor(p - 1)~; if (f[1, length(f)]==5, write("b061599.txt", n++, " ", p)) ) } \\ Harry J. Smith, Jul 25 2009
  • PARI
    list(lim)=my(v=List(), s, t); lim\=1; lim--; for(i=1, logint(lim\2, 5), t=2*5^i; for(j=0, logint(lim\t, 3), s=t*3^j; while(s<=lim, if(isprime(s+1), listput(v, s+1)); s<<=1))); Set(v) \\ Charles R Greathouse IV, Oct 29 2018

Formula

Primes of the form 2^a*3^b*5^c + 1 with a and c > 0.

A061638 Primes p such that the greatest prime divisor of p-1 is 7.

Original entry on oeis.org

29, 43, 71, 113, 127, 197, 211, 281, 337, 379, 421, 449, 491, 631, 673, 701, 757, 883, 1009, 1051, 1373, 1471, 2017, 2269, 2521, 2647, 2689, 2801, 3137, 3361, 3529, 4201, 4481, 5881, 6301, 7001, 7057, 7351, 7561, 7841, 8233, 8821, 10501, 10753, 12097
Offset: 1

Views

Author

Labos Elemer, Jun 13 2001

Keywords

Comments

Prime numbers n for which cos(2*Pi/n) is an algebraic number of 7th degree. - Artur Jasinski, Dec 13 2006

Examples

			For n = {4, 8, 9, 12}, a(n)-1 = {70, 210, 280, 420} = 7*{10, 30, 40, 60}.

Links

Crossrefs

The 4th in a family of sequences after A019434(=Fermat-primes), A058383, A061599.
Cf. A019434, A058383, A023503, A034694, A006530, A006093, A035095, A061599.
Cf. A004729, A058383, A125867-A125875, A024899.

Programs

  • Mathematica
    Select[Prime[Range[2000]],FactorInteger[#-1][[-1,1]] ==7&]  (* Harvey P. Dale, Mar 12 2011 *)
  • PARI
    default(primelimit, 108864001); n=0; forprime (p=3, 108864001, f=factor(p - 1)~; if (f[1, length(f)]==7, write("b061638.txt", n++, " ", p))) \\ Harry J. Smith, Jul 25 2009
  • PARI
    list(lim)=my(v=List(), t, t5, t7); lim\=1; lim--; for(a=1, logint(lim\2, 7), t7=2*7^a; for(b=0, logint(lim\t7, 5), t5=5^b*t7; for(c=0, logint(lim\t5, 3), t=3^c*t5; while(t<=lim, if(isprime(t+1), listput(v, t+1)); t<<=1)))); Set(v) \\ Charles R Greathouse IV, Oct 29 2018

Formula

Primes of form 2^a*3^b*5^c*7^d + 1 with a and d > 1.
Showing 1-3 of 3 results.

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