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

Author

Eric Angelini and Reinhard Zumkeller, May 23 2015

Keywords

• nonn
• base
• look
• hear

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.

Crossrefs

Cf. A008585, A258188, A258217, A258225.

Programs

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

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 *)

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