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.

Previous Showing 11-14 of 14 results.

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.

A058321 Number of x such that phi(x) = 2^n.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32
Offset: 0

Views

Author

Labos Elemer, Dec 11 2000

Keywords

Comments

If there are only 5 Fermat primes (A019434), then a(n) = 32 for n > 31. - T. D. Noe, Jun 21 2012 [Corrected by Jeppe Stig Nielsen, Oct 02 2021.]
The first unknown term is a(8589934592) which depends on whether A000215(33) is composite or prime. - Jeppe Stig Nielsen, Oct 02 2021

Examples

			For n = 0, a(0) = 2 because phi(1) = phi(2) = 1.
For n = 5, invphi(32) gives 7 values as follows: phi({51,64,68,80,96,102,120}) = {32,32,32,32,32,32,32}.

Links

Crossrefs

Cf. A000010, A000079, A003401, A004729, A014197, A019434, A045544, A058213.

Programs

  • Maple
    with(numtheory):[seq(nops(invphi(2^i)),i=1..100)];
  • PARI
    a(n) = invphiNum(1 << n); \\ Amiram Eldar, Nov 15 2024 using Max Alekseyev's invphi.gp

Formula

a(n) = A014197(2^n) = A014197(A000079(n)).

Extensions

Added a(0) and corrected a(31) - T. D. Noe, Jun 21 2012
Correction of a(31) reverted; true value is a(31) = 33. - Jeppe Stig Nielsen, Oct 02 2021

A003527 Divisors of 2^16 - 1.

Original entry on oeis.org

1, 3, 5, 15, 17, 51, 85, 255, 257, 771, 1285, 3855, 4369, 13107, 21845, 65535
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Subset of A004729 because 2^32 - 1 = (2^16 + 1)*(2^16 - 1). - R. J. Mathar, May 24 2008

Links

Crossrefs

First entries of A001317.
Row n = 16 of A361438.

Programs

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.
Previous Showing 11-14 of 14 results.

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

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