A137146 -id:A137146 - cp's OEIS frontend

A137147 Numbers k such that k and k^2 use only the digits 5, 6, 7, 8 and 9.

76, 87, 766, 887, 7666, 8887, 9786, 76587, 76666, 87576, 759576, 766666, 869866, 869867, 886886, 888587, 988866, 7666666, 8766867, 8885887, 76587576, 76666666, 76789686, 86998666, 87565786, 87685676, 88766867, 97759786, 97957576, 766666666, 875765766, 886885887, 887579686, 977699687

Offset: 1

Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008

Generated with DrScheme.

			989878759589576^2 = 979859958686597599779967859776.

Jonathan Wellons, Table of n, a(n) for n = 1..183
J. Wellons, Tables of Shared Digits [archived]
OEIS Index to sequences related to squares.

Cf. A136808, A136809, ..., A137146 for other digit combinations.
Cf. A000290 (the squares); A027675, A058411, ..., A058474 (3-digit combinations).
Cf. A277959, A277960, A277961, A295005, ..., A295009 (squares with largest digit = 2, 3, 4, 5, ..., 9).

A154635 Ratio of the sum of the bends of the 5-dimensional spheres added in the n-th generation of Apollonian packing to the sum of the bends of the initial configuration of seven mutually tangent spheres.

Original entry on oeis.org

1, 2, 15, 108, 774, 5544, 39708, 284400, 2036952, 14589216, 104492016, 748400832, 5360254560, 38391631488, 274971524544, 1969422407424, 14105550112128, 101027866452480, 723589630947072, 5182549848861696, 37118861005211136, 265855588948518912

Offset: 0

Colin Mallows, Jan 13 2009

			Starting with seven 5-dimensional spheres with bends 0,0,1,1,1,1,1 summing to 5, the first derived generation has seven spheres, with bends 1,1,1,1,1,5/2,5/2 summing to 10. So a(1) = 10/5 = 2.

Colin Barker, Table of n, a(n) for n = 0..1000
Colin Mallows, Growing Apollonian packings, J. Integer Sequences v.12, article 09.2.1 (2009).
Index entries for linear recurrences with constant coefficients, signature (8,-6).

Cf. A135849 for dim=2. A137146 for the sum of squares of bends when dim=2. A154636 and A154637 for starting with three spheres in 2 dimensions. A154638-A154645 for results in the three-dimensional case.

CoefficientList[Series[(1 - z) (1 - 5 z)/(1 - 8 z + 6 z^2), {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 03 2011 *)

Vec((1-x)*(1-5*x)/(1-8*x+6*x^2) + O(x^30)) \\ Colin Barker, Nov 16 2016

G.f. (1-x)*(1-5*x) / (1-8*x+6*x^2).
From Colin Barker, Nov 16 2016: (Start)
a(n) = (((4-sqrt(10))^n*(-8+sqrt(10))+(4+sqrt(10))^n*(8+sqrt(10))))/(12*sqrt(10)) for n>0.
a(n) = 8*a(n-1) - 6*a(n-2) for n>2.
(End)

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A137147 Numbers k such that k and k^2 use only the digits 5, 6, 7, 8 and 9.

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A154635 Ratio of the sum of the bends of the 5-dimensional spheres added in the n-th generation of Apollonian packing to the sum of the bends of the initial configuration of seven mutually tangent spheres.

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