OFFSET
1,1
COMMENTS
The only primitive terms of the sequence, i.e., not equal to 10 times a smaller term, are 5, 18, 35 and 315.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
G. Villemin, Nombres complémentés (in French).
Index entries for linear recurrences with constant coefficients, signature (0,0,0,10).
FORMULA
a(n+4) = 10 a(n) for all n >= 3.
G.f.: x*(5 + 18*x + 35*x^2 + 50*x^3 + 130*x^4 + 135*x^5) / (1 - 10*x^4). - Colin Barker, Feb 09 2018
EXAMPLE
5 = (10-5), therefore 5 is in the sequence.
18 = (10-1)*(10-8), therefore 18 is in the sequence.
35 = (10-3)*(10-5), therefore 35 is in the sequence.
315 = (10-3)*(10-1)*(10-5), therefore 315 is in the sequence.
If x is in the sequence, then 10*x = concat(x,0) = x*(10-0) is in the sequence.
MATHEMATICA
LinearRecurrence[{0, 0, 0, 10}, {5, 18, 35, 50, 180, 315}, 40] (* Harvey P. Dale, Mar 02 2024 *)
PROG
(PARI) is(n, b=10)={n==prod(i=1, #n=digits(n, b), b-n[i])}
(PARI) a(n)=if(n>6, a((n-3)%4+3)*10^((n-3)\4), [5, 18, 35, 50, 180, 315][n])
(PARI) Vec(x*(5 + 18*x + 35*x^2 + 50*x^3 + 130*x^4 + 135*x^5) / (1 - 10*x^4) + O(x^60)) \\ Colin Barker, Feb 09 2018
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2018
STATUS
approved