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A137299 Square matrix read by antidiagonals: T(m,n) = m-th term in the continued fraction expansion of Pi^n. 2
3, 9, 7, 31, 1, 15, 97, 159, 6, 1, 306, 2, 3, 1, 292, 961, 50, 2, 7, 2, 1, 3020, 2, 1, 3, 1, 47, 1, 9488, 3, 1, 4, 1, 13, 1, 1, 29809, 1, 2, 1, 60, 16539, 2, 8, 2, 93648, 10, 1, 2, 3, 1, 1, 1, 1, 1, 294204, 21, 14, 7, 3, 9, 4, 6, 3, 1, 3, 924269, 55, 15, 1, 1, 2, 1, 23, 7, 1, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The sequence was suggested by Leroy Quet.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..11325 (antidiagonals 1..150 of the array, flattened)
J. S. Markovitch, Coincidence, data compression and Mach's concept of "economy of thought", APRI-PH-2004-12b, June 3 2004.
EXAMPLE
The matrix limited to order 10 is given by matrix(10,10,m,n,contfrac(Pi^n)[m]):
[ 3 9 31 97 306 961 3020 9488 29809 93648]
[ 7 1 159 2 50 2 3 1 10 21]
[ 15 6 3 2 1 1 2 1 14 15]
[ 1 1 7 3 4 1 2 7 1 1]
[ 292 2 1 1 60 3 3 1 9 4]
[ 1 47 13 16539 1 9 2 1 3 2]
[ 1 1 2 1 4 1 10 3 1 1]
[ 1 8 1 6 23 5 4 1 5 3]
[ 2 1 3 7 1 1 1 1 8 2]
[ 1 1 1 6 2 3 1 1 16 1]
MATHEMATICA
A137299list[dmax_]:=With[{a=Array[ContinuedFraction[Pi^(dmax+1-#), #]&, dmax]}, Array[Diagonal[a, #]&, dmax, 1-dmax]]; A137299list[10] (* Generates 10 antidiagonals *) (* Paolo Xausa, Nov 14 2023 *)
PROG
(PARI) concat(vector(20, i, vector(i, j, contfrac(Pi^(i-j+1))[j])))
(PARI) T(m, n)=contfrac(Pi^n)[m]
CROSSREFS
Sequence in context: A220654 A302158 A337974 * A329238 A001226 A338402
KEYWORD
nonn,easy,tabl
AUTHOR
M. F. Hasler, Mar 14 2008
STATUS
approved

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Last modified June 20 22:01 EDT 2024. Contains 373532 sequences. (Running on oeis4.)