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A042934
Numerators of continued fraction convergents to sqrt(999).
5
31, 32, 63, 95, 158, 885, 5468, 6353, 37233, 80819, 441328, 522147, 3574210, 18393197, 21967407, 40360604, 62328011, 102688615, 6429022141, 6531710756, 12960732897, 19492443653, 32453176550
OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 205377230, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
a(n) = 205377230*a(n-18) - a(n-36). - Wesley Ivan Hurt, May 28 2021
MATHEMATICA
Numerator[Convergents[Sqrt[999], 30]] (* Vincenzo Librandi, Dec 10 2013 *)
PROG
(PARI) A42934=contfracpnqn(c=contfrac(sqrt(999)), #c)[1, ][^-1] \\ Discard possibly incorrect last element. NB: a(n) = A42934[n+1]! For more terms, use:
A042934(n)={n<#A42934 || A42934_upto(n+10); A42934[n+1]}
{A42934_upto(N, A=Vec(A42934, N))=for(n=#A42934+1, N, A[n]=205377230*A[n-18]-A[n-36]); A42934=A} \\ M. F. Hasler, Nov 01 2019
CROSSREFS
Cf. A042935 (denominators).
Analog for other sqrt(m): A001333 (m=2), A002531 (m=3), A001077 (m=5), A041006 (m=6), A041008 (m=7), A041010 (m=8), A005667 (m=10), A041014 (m=11), ..., A042936 (m=1000).
Sequence in context: A133782 A022401 A042936 * A042930 A042932 A042928
KEYWORD
nonn,frac,easy
STATUS
approved