A082204 -id:A082204 - cp's OEIS frontend

A082205 Palindromes pertaining to A082204.

1, 22, 232, 3223, 22322, 232232, 3223223, 22322322, 232232232, 3223223223, 22322322322, 232232232232, 3223223223223, 22322322322322, 232232232232232, 3223223223223223, 22322322322322322, 232232232232232232, 3223223223223223223

Offset: 1

Amarnath Murthy, Apr 10 2003

Perhaps no digits other than 1,2 and 3 occur. From the second term onwards the periodic pattern of two 2's followed by a 3 holds.

			The first six palindromes are:  1, 22, 232, 3223,22322, 232232.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 1001, 0, 0, -1000).

Cf. A082204, A082206.

Join[{1},LinearRecurrence[{0, 0, 1001, 0, 0, -1000},{22, 232, 3223, 22322, 232232, 3223223},18]] (* Ray Chandler, Aug 25 2015 *)

More terms from Joshua Zucker, May 08 2006

A082206 Digit sum of A082205(n).

Original entry on oeis.org

1, 4, 7, 10, 11, 14, 17, 18, 21, 24, 25, 28, 31, 32, 35, 38, 39, 42, 45, 46, 49, 52, 53, 56, 59, 60, 63, 66, 67, 70, 73, 74, 77, 80, 81, 84, 87, 88, 91, 94, 95, 98, 101, 102, 105, 108, 109, 112, 115, 116, 119, 122, 123, 126, 129, 130, 133, 136, 137, 140, 143, 144

Offset: 1

Amarnath Murthy, Apr 10 2003

			The first six palindromes are 1, 22, 232, 3223, 22322, 232232.

G. C. Greubel, Table of n, a(n) for n = 1..5000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Cf. A007953, A082204, A082205.

Essentially the same as A047342.

R:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+3*x+3*x^2+2*x^3-2*x^4)/((1-x)*(1-x^3)) )); // G. C. Greubel, Jan 22 2024

CoefficientList[Series[(1+3x+3x^2+2x^3-2x^4)/((1-x)*(1-x^3)),{x,0,70}],x] (* Vladimir Joseph Stephan Orlovsky, Jan 26 2012 *)
Join[{1},LinearRecurrence[{1, 0, 1, -1},{4, 7, 10, 11},61]] (* Ray Chandler, Aug 25 2015 *)

def a(n): # a = A082206
    if n<5: return 3*n-2
    else: return a(n-3) + 7
[a(n) for n in range(1,71)] # G. C. Greubel, Jan 22 2024

For n>1, a(n+3) = a(n) + 7.
a(n) = A007953(A082205(n)).
G.f.: x*(1 + 3*x + 3*x^2 + 2*x^3 - 2*x^4)/((1-x)*(1-x^3)). - Vladimir Joseph Stephan Orlovsky, Jan 26 2012
a(n) = -a(n-1) - a(n-2) + 7*(n-1), for n >= 4, with a(n) = 3*n-2 for n < 4. - G. C. Greubel, Jan 22 2024

Edited by Don Reble, Mar 13 2006

Offset corrected by Mohammed Yaseen, Aug 15 2023

cp's OEIS Frontend

A082205 Palindromes pertaining to A082204.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions