login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A048269 First palindrome greater than n+2 in bases n+2 and n. 3
5, 26, 21, 24, 154, 40, 121, 60, 181, 84, 253, 112, 337, 144, 433, 180, 541, 220, 661, 264, 793, 312, 937, 364, 1093, 420, 1261, 480, 1441, 544, 1633, 612, 1837, 684, 2053, 760, 2281, 840, 2521, 924, 2773, 1012, 3037, 1104, 3313, 1200, 3601, 1300, 3901 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

a(2), a(3), a(4) and a(6) must be found explicitly.

LINKS

Colin Barker, Table of n, a(n) for n = 2..1000

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

FORMULA

n even and n >= 8: a(n) = n^2+(n/2+3)n+1 (which is (1 n/2+3 1) in base n and (1 n/2-2 1) in base n+2).

n odd and n >= 5: a(n) = (n+3)/2*n+(n+3)/2 (which is ((n+3)/2 (n+3)/2) in base n and ((n+1)/2 (n+1)/2)) in base n+2).

From Colin Barker, Jun 30 2019: (Start)

G.f.: x^2*(5 + 26*x + 6*x^2 - 54*x^3 + 106*x^4 + 46*x^5 - 283*x^6 - 14*x^7 + 259*x^8 - 81*x^10) / ((1 - x)^3*(1 + x)^3).

a(n) = (5 + (-1)^(1 + n) + 2*(5 + (-1)^n)*n + 2*(2 + (-1)^n)*n^2) / 4 for n>6.

a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>10.

(End)

EXAMPLE

a(15)= (15+3)/2*15+(15+3)/2=144, which is (99) in base 15 and (88) in base 17.

MATHEMATICA

Do[ k = n + 3; While[ RealDigits[ k, n + 2 ][[ 1 ] ] != Reverse[ RealDigits[ k, n + 2 ][[ 1 ] ] ] || RealDigits[ k, n ][[ 1 ] ] != Reverse[ RealDigits[ k, n ][[ 1 ] ] ], k++ ]; Print[ k ], {n, 2, 50} ]

PROG

(PARI) Vec(x^2*(5 + 26*x + 6*x^2 - 54*x^3 + 106*x^4 + 46*x^5 - 283*x^6 - 14*x^7 + 259*x^8 - 81*x^10) / ((1 - x)^3*(1 + x)^3) + O(x^50)) \\ Colin Barker, Jun 30 2019

CROSSREFS

Cf. A048268.

Sequence in context: A057688 A259207 A300005 * A073069 A042281 A041625

Adjacent sequences:  A048266 A048267 A048268 * A048270 A048271 A048272

KEYWORD

nonn,easy,base

AUTHOR

Ulrich Schimke (ulrschimke(AT)aol.com)

EXTENSIONS

More terms from Robert G. Wilson v, Aug 15 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 13 23:40 EDT 2019. Contains 327983 sequences. (Running on oeis4.)