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A307056 Row n = digits of A025487(n) in primorial base.

%I A307056 #13 Mar 25 2019 04:20:33
%S A307056 1,1,0,2,0,1,0,0,1,1,0,2,0,0,2,2,0,4,0,0,1,0,0,0,1,0,1,0,1,1,0,0,1,3,
%T A307056 0,0,2,0,0,0,2,0,2,0,2,2,0,0,3,1,0,0,4,0,0,0,4,1,1,0,4,4,0,0,6,0,0,0,
%U A307056 6,2,0,0,1,0,0,0,0,1,0,1,0,0,1,1,0,0,0,1,1,2,2,0,1,2,3,0,0,1,5,0,0,0,1,5,4
%N A307056 Row n = digits of A025487(n) in primorial base.
%C A307056 A025487 is the sequence of products of primorials (A002110).
%H A307056 Michael De Vlieger, <a href="/A307056/b307056.txt">Table of n, a(n) for n = 1..10122</a>, (rows 1 <= n <= 1200, flattened).
%H A307056 Michael De Vlieger, <a href="/A307056/a307056.txt">Relation of A307056 with A025487, A002110, and A067255</a>.
%e A307056 First rows of this sequence:
%e A307056    n  A025487(n)  Row n
%e A307056 -------------------------------
%e A307056    1          1   1
%e A307056    2          2   1, 0
%e A307056    3          4   2, 0
%e A307056    4          6   1, 0, 0
%e A307056    5          8   1, 1, 0
%e A307056    6         12   2, 0, 0
%e A307056    7         16   2, 2, 0
%e A307056    8         24   4, 0, 0
%e A307056    9         30   1, 0, 0, 0
%e A307056   10         32   1, 0, 1, 0
%e A307056   11         36   1, 1, 0, 0
%e A307056   12         48   1, 3, 0, 0
%e A307056   13         60   2, 0, 0, 0
%e A307056   14         64   2, 0, 2, 0
%e A307056   15         72   2, 2, 0, 0
%e A307056   16         96   3, 1, 0, 0
%e A307056   17        120   4, 0, 0, 0
%e A307056   18        128   4, 1, 1, 0
%e A307056   19        144   4, 4, 0, 0
%e A307056   20        180   6, 0, 0, 0
%e A307056   21        192   6, 2, 0, 0
%e A307056   22        210   1, 0, 0, 0, 0
%e A307056   ...
%t A307056 f[n_] := {{1}}~Join~Block[{lim = Product[Prime@ i, {i, n}], ww = NestList[Append[#, 1] &, {1}, n - 1], dec}, dec[x_] := Apply[Times, MapIndexed[Prime[First@ #2]^#1 &, x]]; Map[Block[{w = #, k = 1}, Sort@ Prepend[If[Length@ # == 0, #, #[[1]]], Product[Prime@ i, {i, Length@ w}] ] &@ Reap[Do[If[# < lim, Sow[#]; k = 1, If[k >= Length@ w, Break[], k++]] &@ dec Set[w, If[k == 1, MapAt[# + 1 &, w, k], PadLeft[#, Length@ w, First@ #] &@ Drop[MapAt[# + Boole[i > 1] &, w, k], k - 1] ]], {i, Infinity}] ][[-1]] ] &, ww]]; Block[{nn = 10, b}, b = MixedRadix[Reverse@ Prime@ Range@ nn]; Map[IntegerDigits[#, b] &, Union@ Flatten@ f@ nn]]
%Y A307056 Cf. A002110, A002182, A025487.
%K A307056 nonn,base,tabf
%O A307056 1,4
%A A307056 _Michael De Vlieger_, Mar 21 2019