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

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

1,1

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

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

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

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 *)

Prog

(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

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.

Sequence in context: A287312 A240896 A040985 * A374028 A374029 A153128

Adjacent sequences: A061596 A061597 A061598 * A061600 A061601 A061602

Keyword

nonn

Author

Labos Elemer, Jun 13 2001

Status

approved