A177270 -id:A177270 - cp's OEIS frontend

A177274 Periodic sequence: Repeat 1, 2, 3, 4, 5, 6, 7, 8, 9.

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

Offset: 0

Klaus Brockhaus, May 07 2010

Interleaving of A131669 and A131669 without first five terms.
Continued fraction expansion of (684125+sqrt(635918528029))/1033802.
Decimal expansion of 13717421/111111111.
a(n) = A010888(n+1) = A010878(n)+1 = A117230(n+2)-1.
a(n) = A064806(n+1)-n-1.
Essentially first differences of A037123.

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

Cf. A131669 (odd digits followed by positive even digits), A010888 (digital root of n), A010878 (n mod 9), A117230 (1 followed by (repeat 2, 3, 4, 5, 6, 7, 8, 9, 10), offset 1), A064806 (n + digital root of n), A037123, A177270 (decimal expansion of (684125+sqrt(635918528029))/1033802).

&cat[ [1, 2, 3, 4, 5, 6, 7, 8, 9]: k in [1..12] ];

PadRight[{},120,Range[9]] (* Paolo Xausa, Jan 08 2024 *)

a(n) = (n mod 9)+1.
a(n) = a(n-9) for n > 8; 1; a(n) = n+1 for n <= 8.
G.f.: (1+2*x+3*x^2+4*x^3+5*x^4+6*x^5+7*x^6+8*x^7+9*x^8)/(1-x^9). [corrected by Georg Fischer, May 11 2019]

A177271 Decimal expansion of sqrt(635918528029).

Original entry on oeis.org

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

Offset: 6

Klaus Brockhaus, May 07 2010

Continued fraction expansion of sqrt(635918528029) is 797445 followed by (repeat 398722, 1, 1, 398722, 1594890).

sqrt(635918528029) = sqrt(17)*sqrt(53)*sqrt(193)*sqrt(3656953).

			sqrt(635918528029) = 797445.00000250800995679558...

Daniel Starodubtsev, Table of n, a(n) for n = 6..10000

Cf. A010473 (decimal expansion of sqrt(17)), A010506 (decimal expansion of sqrt(53)), A177272 (decimal expansion of sqrt(193)), A177273 (decimal expansion of sqrt(3656953)), A177274 (continued fraction expansion of (684125+sqrt(635918528029))/1033802), A177270 (decimal expansion of (684125+sqrt(635918528029))/1033802).

First[RealDigits[Sqrt[635918528029],10,120]] (* Paolo Xausa, Jan 09 2024 *)

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 *)

cp's OEIS Frontend

A177274 Periodic sequence: Repeat 1, 2, 3, 4, 5, 6, 7, 8, 9.

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A177271 Decimal expansion of sqrt(635918528029).

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

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