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%I #29 Jun 13 2015 00:53:13
%S 1,5,11,79,175,1259,2789,20065,44449,319781,708395,5096431,11289871,
%T 81223115,179929541,1294473409,2867582785,20630351429,45701395019,
%U 328791149455,728354737519,5240028039851,11607974405285,83511657488161,184999235747041,1330946491770725
%N Solutions to the simultaneous equations m(n)+1=a(n)^2 and 7*m(n)+1=b(n)^2.
%C The equations are equivalent to the Pell equation x(n)^2-7*y(n)^2=9 with x(n)=7*m(n)+4 and y(n)=a(n)*b(n).
%C x-values in the solution to 7x^2 - 6 = y^2.
%C Primes in the sequence are 5, 11, 79, 1259, 2789, 44449, 11289871, 20630351429, ...- _R. J. Mathar_, May 09 2013
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,16,0,-1).
%F From _Bruno Berselli_, Oct 28 2011: (Start)
%F G.f.: x*(1-x)*(1+6*x+x^2)/(1-16*x^2+x^4).
%F a(n) = ((7+(-1)^n*t)*(8-3*t)^floor(n/2)+(7-(-1)^n*t)*(8+3*t)^floor(n/2))/14 with t=sqrt(7). (End)
%F a(n) = 16*a(n-2) - a(n-4) with a(1)=1, a(2)=5, a(3)=11, a(4)=79. - _Sture Sjöstedt_, Nov 18 2011
%p n=0: for a from 1 to 1000000 do b:=sqrt(7*a^2-6):
%p if (trunc(b)=b) then n:=n+1: m:=a^2-1: x:=7*m+4: y:=a*b:
%p print(n,a,b,m,x,y): end if: end do:
%o (Maxima) makelist(expand(((7+(-1)^n*sqrt(7))*(8-3*sqrt(7))^floor(n/2)+(7-(-1)^n*sqrt(7))*(8+3*sqrt(7))^floor(n/2))/14),n,1,26); \\ _Bruno Berselli_, Oct 28 2011
%o (PARI) Vec((1-x)*(1+6*x+x^2)/(1-16*x^2+x^4)+O(x^99)) \\ _Charles R Greathouse IV_, Oct 28 2011
%Y Cf. A195878.
%K nonn,easy
%O 1,2
%A _Paul Weisenhorn_, Jun 20 2009
%E More terms from _Bruno Berselli_, Oct 28 2011
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