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A047341
Numbers that are congruent to {3, 4} mod 7.
9
3, 4, 10, 11, 17, 18, 24, 25, 31, 32, 38, 39, 45, 46, 52, 53, 59, 60, 66, 67, 73, 74, 80, 81, 87, 88, 94, 95, 101, 102, 108, 109, 115, 116, 122, 123, 129, 130, 136, 137, 143, 144, 150, 151, 157, 158, 164, 165, 171
OFFSET
1,1
COMMENTS
Numbers m such that m^2 == 2 (mod 7). - Vincenzo Librandi, Aug 05 2010
Numbers k such that A056107(k)/7 is an integer. - Bruno Berselli, Feb 14 2017
FORMULA
a(n)^2 = 7*A056834(a(n)) + 2. - Bruno Berselli, Nov 28 2010
G.f.: x*(3 + x + 3*x^2)/((1 + x)*(1 - x)^2). - R. J. Mathar, Oct 08 2011
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi*tan(Pi/14)/7. - Amiram Eldar, Dec 12 2021
E.g.f.: 3 + ((14*x - 7)*exp(x) - 5*exp(-x))/4. - David Lovler, Sep 01 2022
From Amiram Eldar, Nov 22 2024: (Start)
Product_{n>=1} (1 - (-1)^n/a(n)) = 1.
Product_{n>=1} (1 + (-1)^n/a(n)) = 2*cos(Pi/7) - 1 (A160389 - 1). (End)
MATHEMATICA
LinearRecurrence[{1, 1, -1}, {3, 4, 10}, 50] (* Amiram Eldar, Dec 12 2021 *)
PROG
(PARI) a(n) = (14*n-5*(-1)^n-7)/4 \\ Charles R Greathouse IV, Jun 11 2015
CROSSREFS
KEYWORD
nonn,easy,changed
STATUS
approved