Displaying 1-10 of 36 results found.
Boustrophedon transform of the continued fraction of e ( A003417).
+20
1
2, 3, 6, 14, 35, 116, 448, 1980, 10098, 57840, 368201, 2578384, 19697486, 163017000, 1452918806, 13874348700, 141322966623, 1529472867448, 17526468199148, 211996227034964, 2699219798770446, 36085910558435148, 505406091697374877
Decimal expansion of the number which results when the Boustrophedon transform of the continued fraction of e ( A080408, A003417) is interpreted as a continued fraction.
+20
1
2, 3, 1, 5, 9, 8, 4, 7, 3, 6, 1, 5, 7, 8, 9, 1, 3, 8, 3, 3, 7, 8, 5, 9, 5, 3, 5, 0, 9, 2, 0, 4, 0, 6, 8, 1, 6, 1, 7, 4, 4, 9, 6, 8, 5, 7, 3, 8, 1, 3, 5, 7, 7, 6, 4, 3, 4, 2, 2, 0, 8, 1, 7, 7, 1, 2, 1, 0, 1, 9, 5, 9, 8, 7, 2, 8, 7, 6, 9, 0, 1, 2, 7, 4, 5, 7, 1, 9, 8, 7, 0, 1, 3, 2, 2, 3, 8, 5, 3, 5
Decimal expansion of e.
(Formerly M1727 N0684)
+10
661
2, 7, 1, 8, 2, 8, 1, 8, 2, 8, 4, 5, 9, 0, 4, 5, 2, 3, 5, 3, 6, 0, 2, 8, 7, 4, 7, 1, 3, 5, 2, 6, 6, 2, 4, 9, 7, 7, 5, 7, 2, 4, 7, 0, 9, 3, 6, 9, 9, 9, 5, 9, 5, 7, 4, 9, 6, 6, 9, 6, 7, 6, 2, 7, 7, 2, 4, 0, 7, 6, 6, 3, 0, 3, 5, 3, 5, 4, 7, 5, 9, 4, 5, 7, 1, 3, 8, 2, 1, 7, 8, 5, 2, 5, 1, 6, 6, 4, 2, 7, 4, 2, 7, 4, 6
Denominators of convergents to e.
(Formerly M2343)
+10
34
1, 1, 3, 4, 7, 32, 39, 71, 465, 536, 1001, 8544, 9545, 18089, 190435, 208524, 398959, 4996032, 5394991, 10391023, 150869313, 161260336, 312129649, 5155334720, 5467464369, 10622799089, 196677847971, 207300647060, 403978495031, 8286870547680, 8690849042711
CROSSREFS
Cf. A003417 (continued fraction of e).
Numerators of convergents to e.
(Formerly M0869)
+10
28
2, 3, 8, 11, 19, 87, 106, 193, 1264, 1457, 2721, 23225, 25946, 49171, 517656, 566827, 1084483, 13580623, 14665106, 28245729, 410105312, 438351041, 848456353, 14013652689, 14862109042, 28875761731, 534625820200, 563501581931, 1098127402131, 22526049624551
CROSSREFS
Cf. A003417 (continued fraction of e).
A generalized continued fraction for Euler's number e.
+10
7
1, 0, 1, 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1, 12, 1, 1, 14, 1, 1, 16, 1, 1, 18, 1, 1, 20, 1, 1, 22, 1, 1, 24, 1, 1, 26, 1, 1, 28, 1, 1, 30, 1, 1, 32, 1, 1, 34, 1, 1, 36, 1, 1, 38, 1, 1, 40, 1, 1, 42
COMMENTS
Only a(1) = 0 prevents this from being a simple continued fraction. The motivation for this alternate representation is that the simple pattern {1, 2*n, 1} (from n=0) may be more mathematically appealing than the pattern in the corresponding simple continued fraction (at A003417). - Joseph Biberstine (jrbibers(AT)indiana.edu), Aug 14 2006
Continued fraction for e^2.
(Formerly M4322 N1811)
+10
6
7, 2, 1, 1, 3, 18, 5, 1, 1, 6, 30, 8, 1, 1, 9, 42, 11, 1, 1, 12, 54, 14, 1, 1, 15, 66, 17, 1, 1, 18, 78, 20, 1, 1, 21, 90, 23, 1, 1, 24, 102, 26, 1, 1, 27, 114, 29, 1, 1, 30, 126, 32, 1, 1, 33, 138, 35, 1, 1, 36, 150, 38, 1, 1, 39, 162, 41, 1, 1, 42, 174, 44, 1, 1, 45, 186, 47, 1, 1
a(n) = floor(e^e^ ... ^e), with n e's.
+10
6
"Exact" continued fraction of e.
+10
6
3, -4, 2, 5, -2, -7, 2, 9, -2, -11, 2, 13, -2, -15, 2, 17, -2, -19, 2, 21, -2, -23, 2, 25, -2, -27, 2, 29, -2, -31, 2, 33, -2, -35, 2, 37, -2, -39, 2, 41, -2, -43, 2, 45, -2, -47, 2, 49, -2, -51, 2, 53, -2, -55, 2, 57, -2, -59, 2, 61, -2, -63, 2, 65, -2, -67, 2, 69, -2, -71, 2, 73, -2, -75, 2, 77, -2, -79, 2, 81, -2, -83, 2, 85, -2, -87, 2
Continued fraction for e^e^e A073227.
+10
5
3814279, 9, 1, 1, 4, 1, 53, 26, 1, 13, 3, 1, 1, 22, 1, 226, 1, 5, 2, 1, 6, 2, 3, 1, 4, 1, 6, 39, 2, 1, 3, 1, 5, 1, 4, 1, 3, 1, 4, 1, 1, 19, 1, 2, 8899, 5, 2, 2, 1, 3, 3, 2, 2, 2, 1, 1, 3, 5, 1, 6, 10, 2, 1, 2, 1, 1, 1, 2, 2, 4, 1, 10, 2, 6, 1, 5, 6, 2, 4, 2, 1, 2, 1, 1, 1, 3, 2, 2, 1, 1, 11, 7, 3, 1, 4, 4
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