|
| |
|
|
A061638
|
|
Primes p such that the greatest prime divisor of p-1 is 7.
|
|
1
| |
|
|
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
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Prime numbers n for which cos(2pi/n) is an algebraic number of 7-th degree. - Artur Jasinski (grafix(AT)csl.pl), Dec 13 2006
|
|
|
LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,500
|
|
|
FORMULA
| Primes of form (2^a)*(3^b)*(5^c)*(7^d)+1.
|
|
|
EXAMPLE
| For n = {4, 8, 9, 12}, a(n)-1 = {70, 210, 280, 420} = 7*{10, 30, 40, 60}.
|
|
|
MATHEMATICA
| Do[If[Take[FactorInteger[EulerPhi[2n + 1]][[ -1]], 1] == {7} && PrimeQ[2n + 1], Print[2n + 1]], {n, 1, 10000}] - Artur Jasinski (grafix(AT)csl.pl), Dec 13 2006
Select[Prime[Range[2000]], FactorInteger[#-1][[-1, 1]] ==7&] (* From 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)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 25 2009]
|
|
|
CROSSREFS
| The 4-th 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 E. (labos(AT)ana.sote.hu), Jun 13 2001
|
| |
|
|
