This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A276328 #29 May 20 2021 10:15:26
%S A276328 0,1,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,1,2,3,4,2,3,4,5,3,4,5,6,4,5,6,7,
%T A276328 5,6,2,3,4,5,3,4,5,6,4,5,6,7,5,6,7,8,6,7,3,4,5,6,4,5,6,7,5,6,7,8,6,7,
%U A276328 8,9,7,8,4,5,6,7,5,6,7,8,6,7,8,9,7,8,9,10,8,9,5,6,7,8,6,7,1
%N A276328 Digit sum when n is expressed in greedy A001563-base (A276326).
%C A276328 a(n) is the number of terms of A001563 needed to sum to n using the greedy algorithm.
%C A276328 This seems to give also the minimal number of terms of A001563 that sum to n (checked empirically up to n=3265920), but it would be nice to know for sure whether this holds for all n.
%H A276328 Antti Karttunen, <a href="/A276328/b276328.txt">Table of n, a(n) for n = 0..4320</a>
%F A276328 a(0) = 0; for n >= 1, a(n) = 1 + a(n-A258199(n)).
%F A276328 a(0) = 0; for n >= 1, a(n) = A276333(n) + a(A276335(n)).
%F A276328 Other identities and observations. For all n >= 0:
%F A276328 a(A276091(n)) = A000120(n).
%F A276328 a(n) >= A276337(n).
%F A276328 It also seems that a(n) <= A276332(n) for all n.
%e A276328 For n=1, the largest term of A001563 <= 1 is A001563(1) = 1, thus a(1) = 1.
%e A276328 For n=2, the largest term of A001563 <= 2 is A001563(1) = 1, thus a(2) = 1 + a(2-1) = 2.
%e A276328 For n=18, the largest term of A001563 <= 18 is A001563(3) = 18, thus a(18) = 1.
%e A276328 For n=20, the largest term of A001563 <= 20 is A001563(3) = 18, thus a(20) = 1 + a(20-18) = 3.
%e A276328 For n=36, the largest term of A001563 <= 36 is A001563(3) = 18, thus a(36) = 1 + a(18) = 2.
%t A276328 f[n_] := Block[{a = {{0, n}}}, Do[AppendTo[a, {First@ #, Last@ #} &@ QuotientRemainder[a[[-1, -1]], (# #!) &[# - i]]], {i, 0, # - 1}] &@NestWhile[# + 1 &, 0, (# #!) &[# + 1] <= n &]; Rest[a][[All, 1]]]; {0}~Join~Table[Total@ f@ n, {n, 120}] (* _Michael De Vlieger_, Aug 31 2016 *)
%o A276328 (Scheme, with memoization-macro definec, two versions)
%o A276328 (definec (A276328 n) (if (zero? n) n (+ 1 (A276328 (- n (A258199 n))))))
%o A276328 (definec (A276328 n) (if (zero? n) n (+ (A276333 n) (A276328 (A276335 n)))))
%o A276328 ;; Third version which explicitly searches a minimal representation of n as a sum of terms of A001563 (but please see the comment):
%o A276328 (definec (A276328_by_minimization n) (if (zero? n) n (let loop ((i (A258198 n)) (m #f)) (cond ((zero? i) m) ((not m) (loop (- i 1) (+ 1 (A276328_by_minimization (- n (A001563 i)))))) (else (loop (- i 1) (min m (+ 1 (A276328_by_minimization (- n (A001563 i)))))))))))
%Y A276328 Cf. A001563, A258199.
%Y A276328 Cf. A000120, A276329, A276330, A276332, A276333, A276335.
%Y A276328 Cf. A276091 (gives all n for which a(n) = A276337(n)).
%Y A276328 Cf. also A007895, A034968, A265744, A265745 for similar sequences.
%K A276328 nonn,base
%O A276328 0,3
%A A276328 _Antti Karttunen_, Aug 30 2016