OFFSET
0,2
COMMENTS
Original definition: Numbers whose base 8 or octal representation is 6666666......6.
Also: after 0 and 6, always append the least nonnegative integer not occurring earlier such that the concatenation of the binary representation of all terms is a palindrome. If the initial terms are not imposed, this gives (0, 1, 2, 6, 54, ...). It might be more natural to use offset 0 for both of these sequences. - M. F. Hasler, Sep 20 2025
LINKS
M. F. Hasler, Table of n, a(n) for n = 0..1000 (initially from G. C. Greubel with offset 1), Sep 26 2025
Index entries for linear recurrences with constant coefficients, signature (9,-8).
FORMULA
a(n) = 6*(8^n - 1)/7 = 6*A023001(n).
a(n) = 8*a(n-1) + 6 for n>0, a(0) = 0. - Vincenzo Librandi, Oct 03 2010
G.f.: 6*x/( (1-x)*(1-8*x) ). - R. J. Mathar, Oct 07 2016
E.g.f.: 6*(exp(8*x) - exp(x))/7. - G. C. Greubel, Aug 03 2019
a(n) = A083068(n) - 1. - Alois P. Heinz, May 20 2023
MAPLE
seq(6*(8^n-1)/7, n=0..30);
MATHEMATICA
FromDigits[#, 8]&/@Table[Table[6, {i}], {i, 0, 30}] (* Harvey P. Dale, Mar 19 2011 *)
6*(8^Range[0, 30]-1)/7 (* G. C. Greubel, Aug 03 2019 *)
PROG
(PARI) vector(30, n, 6*(8^(n-1)-1)/7) \\ G. C. Greubel, Aug 03 2019
(PARI) apply( {A125837(n)=8^n\7*6}, [0..30]) \\ M. F. Hasler, Sep 26 2025
(Magma) [6*(8^n-1)/7: n in [0..30]]; // G. C. Greubel, Aug 03 2019
(SageMath) [6*(8^n-1)/7 for n in (0..30)] # G. C. Greubel, Aug 03 2019
(GAP) List([0..30], n-> 6*(8^n-1)/7); # G. C. Greubel, Aug 03 2019
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Zerinvary Lajos, Feb 03 2007
EXTENSIONS
Offset 0 restored and correspondingly edited by M. F. Hasler, Sep 26 2025
STATUS
approved