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

Author

Klaus Brockhaus, May 07 2010

Keywords

• cofr
• easy
• nonn

Comments

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.

Links

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

Crossrefs

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).

Programs

Magma

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

Mathematica

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

Formula

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]