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A276337
Number of nonzero digits in greedy A001563-base representation of n (A276326).
5
0, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 1, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 4, 4
OFFSET
0,6
LINKS
FORMULA
a(0) = 0; for n >= 1, a(n) = 1 + a(A276335(n)).
For all n >= 0, a(n) <= A276328(n).
MATHEMATICA
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[Count[f@ n, d_ /; d > 0], {n, 120}] (* Michael De Vlieger, Aug 31 2016 *)
PROG
(Scheme, with memoization-macro definec)
(definec (A276337 n) (if (zero? n) n (+ 1 (A276337 (A276335 n)))))
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Aug 30 2016
STATUS
approved