A177034 -id:A177034 - cp's OEIS frontend

A010887 Simple periodic sequence: repeat 1,2,3,4,5,6,7,8.

1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1

Offset: 0

N. J. A. Sloane

Partial sums are given by A130486(n)+n+1. - Hieronymus Fischer, Jun 08 2007

1371742/11111111 = 0.123456781234567812345678... - Eric Desbiaux, Nov 03 2008

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1).

Cf. A010872, A010873, A010874, A010875, A010876, A010878, A004526, A002264, A002265, A002266.

Cf. A177034 (decimal expansion of (9280+3*sqrt(13493990))/14165). - Klaus Brockhaus, May 01 2010

a010887 = (+ 1) . flip mod 8
a010887_list = cycle [1..8]
-- Reinhard Zumkeller, Nov 09 2014, Mar 04 2014

PadRight[{},90,Range[8]] (* Harvey P. Dale, May 10 2022 *)

def A010887(n): return 1 + (n & 7) # Chai Wah Wu, May 25 2022

a(n) = 1 + (n mod 8) - Paolo P. Lava, Nov 21 2006
From Hieronymus Fischer, Jun 08 2007: (Start)
a(n) = (1/2)*(9 - (-1)^n - 2*(-1)^(b/4) - 4*(-1)^((b - 2 + 2*(-1)^(b/4))/8)) where b = 2n - 1 + (-1)^n.
Also a(n) = A010877(n) + 1.
G.f.: g(x) = (1/(1-x^8))*Sum_{k=0..7} (k+1)*x^k.
Also: g(x) = (8x^9 - 9x^8 + 1)/((1-x^8)*(1-x)^2). (End)

A177933 Decimal expansion of (232405+sqrt(71216963807))/348378.

Original entry on oeis.org

1, 4, 3, 3, 1, 2, 7, 4, 2, 6, 7, 2, 2, 2, 9, 1, 1, 3, 0, 6, 9, 3, 4, 5, 3, 5, 5, 4, 9, 7, 5, 2, 3, 5, 5, 5, 7, 3, 6, 9, 3, 4, 0, 0, 8, 4, 0, 6, 9, 9, 9, 7, 1, 4, 6, 6, 5, 9, 6, 4, 6, 7, 0, 3, 1, 7, 6, 1, 3, 7, 8, 0, 1, 6, 6, 3, 2, 3, 6, 8, 1, 2, 3, 2, 5, 7, 5, 9, 2, 8, 7, 6, 3, 6, 4, 5, 9, 6, 2, 1, 6, 8, 8, 9, 9

Offset: 1

Klaus Brockhaus, May 15 2010

Continued fraction expansion of (232405+sqrt(71216963807))/348378 is A010889.

Agrees with A060997 for n < 14, with A177270 for n < 13, with A177034 for n < 11, with A177160 for n < 9.

			(232405+sqrt(71216963807))/348378 = 1.43312742672229113069...

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A177934 (decimal expansion of sqrt(71216963807)), A010889 (repeat 1, 2, 3, 4, 5, 6, 7, 8, 9, 10), A060997 (decimal representation of continued fraction 1, 2, 3, 4, 5, 6, 7, ...), A177270 (decimal expansion of (684125+sqrt(635918528029))/1033802), A177034 (decimal expansion of (9280+3*sqrt(13493990))/14165), A177160 (decimal expansion of (4502+sqrt(29964677))/6961).

First[RealDigits[(232405+Sqrt[71216963807])/348378,10,120]] (* Paolo Xausa, Jan 09 2024 *)

A177035 Decimal expansion of sqrt(13493990).

Original entry on oeis.org

3, 6, 7, 3, 4, 1, 6, 6, 6, 5, 7, 2, 1, 4, 3, 7, 0, 5, 1, 3, 6, 6, 9, 3, 6, 1, 5, 1, 9, 2, 0, 9, 7, 7, 4, 5, 9, 8, 4, 5, 4, 1, 6, 4, 1, 0, 5, 9, 3, 4, 2, 3, 5, 3, 2, 4, 9, 6, 8, 0, 7, 4, 3, 0, 1, 6, 2, 4, 1, 9, 7, 3, 8, 8, 0, 7, 0, 9, 6, 9, 5, 4, 7, 0, 3, 5, 4, 9, 9, 2, 6, 8, 7, 7, 3, 9, 0, 7, 4, 2, 8, 7, 9, 9, 2

Offset: 4

Klaus Brockhaus, May 01 2010

Continued fraction expansion of sqrt(13493990) is 3673 followed by (repeat 2, 2, 2, 7346).

sqrt(13493990) = sqrt(2)*sqrt(5)*sqrt(19)*sqrt(29)*sqrt(31)*sqrt(79).

			sqrt(13493990) = 3673.41666572143705136693...

Cf. A002193 (decimal expansion of sqrt(2)), A002163 (decimal expansion of sqrt(5)), A010475 (decimal expansion of sqrt(19)), A010484 (decimal expansion of sqrt(29)), A010486 (decimal expansion of sqrt(31)), A010531 (decimal expansion of sqrt(79)), A177034 (decimal expansion of (9280+3*sqrt(13493990))/14165).

RealDigits[Sqrt[13493990],10,120][[1]] (* Harvey P. Dale, Nov 11 2016 *)

cp's OEIS Frontend

A010887 Simple periodic sequence: repeat 1,2,3,4,5,6,7,8.

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A177933 Decimal expansion of (232405+sqrt(71216963807))/348378.

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A177035 Decimal expansion of sqrt(13493990).

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