A235168 Triangle read by rows: row n gives digits of n in primorial base.

0, 1, 1, 0, 1, 1, 2, 0, 2, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 0, 1, 2, 1, 2, 0, 0, 2, 0, 1, 2, 1, 0, 2, 1, 1, 2, 2, 0, 2, 2, 1, 3, 0, 0, 3, 0, 1, 3, 1, 0, 3, 1, 1, 3, 2, 0, 3, 2, 1, 4, 0, 0, 4, 0, 1, 4, 1, 0, 4, 1, 1, 4, 2, 0, 4, 2, 1, 1, 0, 0, 0

Offset: 0

Author

Reinhard Zumkeller, Jan 05 2014

Keywords

• nonn
• tabf
• base
• look

Comments

T(n,k) = A108731(n,k) for k=0..23.

a(n) = A108731(n) for n=0..63, when both tables are seen as flattened lists.

T(n,k) < 10 for k = 1..A235224(n) and n < 2100 = 10 * 7#.

When read from right to left, the row n gives exponents for successive primes 2, 3, 5, 7, 11, etc., in A276086(n). - Antti Karttunen, Mar 15 2021

Examples

			.        n | .. + _*7# + _*5# + _*3# + _*2# + _*1# | row(n)
. ---------+---------------------------------------+---------------------
.       10 | 1*6 + 2*2 + 0*1                       | [1,2,0], A276086(10) = 5 * 3^2
.      100 | 3*30 + 1*6 + 2*2 + 0*1                | [3,1,2,0]
.     1000 | 4*210 + 5*30 + 1*6 + 2*2n + 0*1       | [4,5,1,2,0]
.     2099 | 9*210 + 6*30 + 4*6 + 2*2 + 1*1        | [9,6,4,2,1]
.     2100 | 10*210 + 0*30 + 0*6 + 0*2 + 0*1       | [10,0,0,0,0]
.    10000 | 4*2310 + 3*210 + 4*30 + 1*6 + 2*2     | [4,3,4,1,2,0]
.   100000 | 3*30030+4*2310+3*210+1*30+1*6+2*2+0*1 | [3,4,3,1,1,2,0]
.  1000000 |                                       | [1,16,3,9,6,1,2,0]
. 10000000 |                                       | [1,0,10,0,0,0,1,2,0]
.  1000000 = 1*510510+16*30030+3*2310+9*210+6*30+1*6+2*2+0*1
. 10000000 = 1*9699690+0*510510+10*30030+0*2310+0*210+0*30+1*6+2*2+0*1
		

Links

• Reinhard Zumkeller, Rows n = 0..2500 of triangle, flattened
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A002110, A049345, A108731, A235224 (row lengths), A276086.

Programs

Haskell

a235168 n k = a235168_row n !! k
a235168_row 0 = [0]
a235168_row n = t n $ reverse $ takeWhile (<= n) a002110_list
   where t 0 []     = []
         t x (b:bs) = x' : t m bs where (x', m) = divMod x b
a235168_tabf = map a235168_row [0..]

Mathematica

row[n_] := Module[{k = n, p = 2, s = {}, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, AppendTo[s, r]; p = NextPrime[p]]; Reverse[s]]; row[0] = {0}; Array[row, 31, 0] // Flatten (* Amiram Eldar, Mar 11 2024 *)