OFFSET
1,1
COMMENTS
Numbers 7*k such that gcd(k,30) = 1.
Numbers congruent to 7, 49, 77, 91, 119, 133, 161, 203 modulo 210. - Jianing Song, Nov 18 2022
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1).
FORMULA
G.f.: 7*x*(x^8 + 6*x^7 + 4*x^6 + 2*x^5 + 4*x^4 + 2*x^3 + 4*x^2 + 6*x + 1) / ((x-1)^2*(x+1)*(x^2+1)*(x^4+1)). - Colin Barker, Feb 24 2013
a(n) = 7*A007775(n).
a(n+8) = a(n) + 210. - Jianing Song, Nov 18 2022
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(23 + sqrt(5) - sqrt(6*(5 + sqrt(5))))*Pi/105. - Amiram Eldar, Jul 15 2023
EXAMPLE
77 is in the sequence because gcd(77, 30) = 1.
84 is not in the sequence because gcd(84, 3) = 6.
91 is in the sequence because gcd(91, 30) = 1.
MAPLE
q:= k-> igcd(k, 30)=1:
select(q, [7*i$i=1..300])[]; # Alois P. Heinz, Feb 25 2020
MATHEMATICA
7Select[ Range[190], GCD[ #, 2*3*5] == 1 & ]
PROG
(PARI) is(n)=gcd(210, n)==7 \\ Charles R Greathouse IV, Aug 05 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert G. Wilson v, Jun 15 2003
STATUS
approved