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

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

1,1

Comments

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

Links

Harry J. Smith and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 500 terms from Smith)

Formula

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

Example

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

Mathematica

Select[Prime[Range[2000]], FactorInteger[#-1][[-1, 1]] ==7&]  (* Harvey P. Dale, Mar 12 2011 *)

Prog

(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

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.

Sequence in context: A140444 A042969 A042967 * A136062 A039348 A043171

Adjacent sequences: A061635 A061636 A061637 * A061639 A061640 A061641

Keyword

nonn

Author

Labos Elemer, Jun 13 2001

Status

approved