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

0,7

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

Links

Reinhard Zumkeller, Rows n = 0..2500 of triangle, flattened

Index entries for sequences related to primorial base.

Example

.        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 .

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 *)

Prog

(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..]

Crossrefs

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

Sequence in context: A076626 A182886 A108731 * A060950 A039976 A287267

Adjacent sequences: A235165 A235166 A235167 * A235169 A235170 A235171

Keyword

nonn,tabf,base,look

Author

Reinhard Zumkeller, Jan 05 2014

Status

approved