A258083 Smallest multiple of 3 not appearing earlier that ends with n.

21, 12, 3, 24, 15, 6, 27, 18, 9, 210, 111, 312, 213, 114, 315, 216, 117, 318, 219, 120, 321, 222, 123, 324, 225, 126, 327, 228, 129, 30, 231, 132, 33, 234, 135, 36, 237, 138, 39, 240, 141, 42, 243, 144, 45, 246, 147, 48, 249, 150, 51, 252, 153, 54, 255, 156

Offset

1,1

Comments

a(10*n) = 10*a(n).

The sequence is a permutation of the positive multiples of 3. - Vladimir Shevelev, May 24 2015

24 ends with 24 but as 24 is the least element divisible by 3 that ends with 4, it's already used and a(24) = 324. Generally, a(n) = k * 10^d + n with k in {0,1,2,3} and d the number of digits of n. - David A. Corneth, May 24 2015

A258225(n) = a(n) / 3 is a permutation of the positive integers. - Reinhard Zumkeller, May 27 2015

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..9999

Éric Angelini, Multiples of 3 ending with n, SeqFan list, May 23 2015.

Mathematica

a[n_] := a[n] = For[k=3, True, k=k+3, If[Divisible[k-n, 10^IntegerLength[n] ] && FreeQ[Array[a, n-1], k], Return[k]]]; Array[a, 56] (* Jean-François Alcover, Feb 06 2018 *)

Prog

(Haskell)
import Data.List (isPrefixOf, delete)
a258083 n = a258083_list !! (n-1)
a258083_list = f 1 $ tail $ zip
   a008585_list $ map (reverse . show) a008585_list where
   f x ws = g ws where
     g ((u, vs) : uvs) = if isPrefixOf xs vs
                         then u : f (x + 1) (delete (u, vs) ws) else g uvs
     xs = reverse $ show x
(PARI) a(n) = {my(d = digits(n), s = vecsum(d), k); if(s%3 > 0, k = (3 - s%3)%3, i=1; while(i < #d && d[i] == 3, i++); if(i<#d && d[i+1] >= 1 && d[i]-1 == bitand(d[i]-1, 1), k = 3)); k*10^#d + n} \\ David A. Corneth, May 24 2015

Crossrefs

Cf. A008585, A258188, A258217, A258225.

Sequence in context: A270790 A300887 A301497 * A260527 A260529 A166033

Adjacent sequences: A258080 A258081 A258082 * A258084 A258085 A258086

Keyword

nonn,base,look,hear

Author

Eric Angelini and Reinhard Zumkeller, May 23 2015

Status

approved