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

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, 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, 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

Offset

1,4

Comments

A025487 is the sequence of products of primorials (A002110).

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10122, (rows 1 <= n <= 1200, flattened).

Michael De Vlieger, Relation of A307056 with A025487, A002110, and A067255.

Example

First rows of this sequence:
   n  A025487(n)  Row n
-------------------------------
   1          1   1
   2          2   1, 0
   3          4   2, 0
   4          6   1, 0, 0
   5          8   1, 1, 0
   6         12   2, 0, 0
   7         16   2, 2, 0
   8         24   4, 0, 0
   9         30   1, 0, 0, 0
  10         32   1, 0, 1, 0
  11         36   1, 1, 0, 0
  12         48   1, 3, 0, 0
  13         60   2, 0, 0, 0
  14         64   2, 0, 2, 0
  15         72   2, 2, 0, 0
  16         96   3, 1, 0, 0
  17        120   4, 0, 0, 0
  18        128   4, 1, 1, 0
  19        144   4, 4, 0, 0
  20        180   6, 0, 0, 0
  21        192   6, 2, 0, 0
  22        210   1, 0, 0, 0, 0
  ...

Mathematica

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]]

Crossrefs

Cf. A002110, A002182, A025487.

Sequence in context: A326642 A087371 A307597 * A112762 A357520 A145171

Adjacent sequences: A307053 A307054 A307055 * A307057 A307058 A307059

Keyword

nonn,base,tabf

Author

Michael De Vlieger, Mar 21 2019

Status

approved