Search: id:A086541
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%I A086541
%S A086541 1,4,9,49,2116,1104601,1220041748025,73506264463383837985201,
%T A086541 152589000107917580345020742323132226398704361,
%U A086541 1669769004292648133509475727812173973930459916514124965718261930975078855532062950740889
%N A086541 a(1) = 1, a(2) = 4; a(n) = smallest square of the form k*a(n-1) + a(n-2).
%C A086541 The sequence is infinite. Proof: In a(n) = k*a(n-1)+a(n-2), One ( and 
               the largest) value of k is a(n-1)-2{a(n-2)}^(1/2). which gives a(n) 
               = {a(n-1)-{a(n-2)^(1/2)}^2.
%e A086541 a(3) = 4*2 +1 = 9, a(4) = 5*9 +4 = 49, a(5) = 43*49 + 9 = 2116= 46^2.
%o A086541 (PARI) A = vector(11); A[1] = 1; A[2] = 2; B = vector(11, i, A[i]^2); 
               for (n = 3, 11, z = znstar(B[n - 1]); l = length(z[2]); c = vector(l, 
               i, z[3][i]^(z[2][i]/2)); v = vector(2^l, i, A[n - 2]*prod(j = 1, 
               l, c[j]^(i\2^(l - j)%2))); v = vecsort(lift(v)); print(B[n - 2],vector(2^l, 
               i, v[i]^2%B[n - 1])); A[n] = if (v[1] == A[n - 2], v[2], v[1]); B[n] 
               = A[n]^2; print(B[n])); (Wasserman)
%Y A086541 Cf. A086542.
%Y A086541 Sequence in context: A053967 A028945 A082875 this_sequence A053965 A058444 
               A053925
%Y A086541 Adjacent sequences: A086538 A086539 A086540 this_sequence A086542 A086543 
               A086544
%K A086541 nonn
%O A086541 1,2
%A A086541 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 23 2003
%E A086541 More terms from Rick L. Shepherd (rshepherd2(AT)hotmail.com), Aug 28 
               2003
%E A086541 More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Mar 21 
               2005

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