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 A161588 The list of the k values in the common solutions to the 2 equations 11*k+1=A^2, 15*k+1=B^2. 1
 0, 13, 2184, 364728, 60907405, 10171171920, 1698524803248, 283643470970509, 47366761127271768, 7909965464783414760, 1320916865857702993165, 220585206632771616443808, 36836408590807002243122784, 6151459649458136602985061133, 1027256925050918005696262086440 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The 2 equations are equivalent to the Pell equation x^2-165*y^2=1, with x=(165*k+13)/2 and y=A*B/2, case C=11 in A160682. LINKS Index entries for linear recurrences with constant coefficients, signature (168,-168,1). FORMULA k(t+3)=168*(k(t+2)-k(t+1))+k(t). k(t)=((13+w)*((167+13*w)/2)^(t-1)+(13-w)*((167-13*w)/2)^(t-1))/330 where w=sqrt(165). k(t) = floor of ((13+w)*((167+13*w)/2)^(t-1))/330; G.f.: -13*x^2/((x-1)*(x^2-167*x+1)). MAPLE t:=0: for n from 0 to 1000000 do a:=sqrt(11*n+1): b:=sqrt(15*n+1): if (trunc(a)=a) and (trunc(b)=b) then t:=t+1: print(t, n, a, b): end if: end do: CROSSREFS Cf. A160682, A085260 (sequence of A), A126816 (sequence of B). Sequence in context: A221823 A075601 A325216 * A221927 A013718 A145187 Adjacent sequences: A161585 A161586 A161587 * A161589 A161590 A161591 KEYWORD nonn,easy AUTHOR Paul Weisenhorn, Jun 14 2009 EXTENSIONS Edited, extended by R. J. Mathar, Sep 02 2009 STATUS approved

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Last modified December 9 19:36 EST 2022. Contains 358703 sequences. (Running on oeis4.)