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%I #26 Mar 11 2024 03:44:07
%S 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,
%T 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,
%U 0,1,4,1,0,4,1,1,4,2,0,4,2,1,1,0,0,0
%N Triangle read by rows: row n gives digits of n in primorial base.
%C 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;
%C T(n,k) < 10 for k = 1..A235224(n) and n < 2100 = 10 * 7#.
%C 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
%H Reinhard Zumkeller, <a href="/A235168/b235168.txt">Rows n = 0..2500 of triangle, flattened</a>
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%e . n | .. + _*7# + _*5# + _*3# + _*2# + _*1# | row(n)
%e . ---------+---------------------------------------+---------------------
%e . 10 | 1*6 + 2*2 + 0*1 | [1,2,0], A276086(10) = 5 * 3^2
%e . 100 | 3*30 + 1*6 + 2*2 + 0*1 | [3,1,2,0]
%e . 1000 | 4*210 + 5*30 + 1*6 + 2*2n + 0*1 | [4,5,1,2,0]
%e . 2099 | 9*210 + 6*30 + 4*6 + 2*2 + 1*1 | [9,6,4,2,1]
%e . 2100 | 10*210 + 0*30 + 0*6 + 0*2 + 0*1 | [10,0,0,0,0]
%e . 10000 | 4*2310 + 3*210 + 4*30 + 1*6 + 2*2 | [4,3,4,1,2,0]
%e . 100000 | 3*30030+4*2310+3*210+1*30+1*6+2*2+0*1 | [3,4,3,1,1,2,0]
%e . 1000000 | | [1,16,3,9,6,1,2,0]
%e . 10000000 | | [1,0,10,0,0,0,1,2,0]
%e . 1000000 = 1*510510+16*30030+3*2310+9*210+6*30+1*6+2*2+0*1
%e . 10000000 = 1*9699690+0*510510+10*30030+0*2310+0*210+0*30+1*6+2*2+0*1 .
%t 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 *)
%o (Haskell)
%o a235168 n k = a235168_row n !! k
%o a235168_row 0 = [0]
%o a235168_row n = t n $ reverse $ takeWhile (<= n) a002110_list
%o where t 0 [] = []
%o t x (b:bs) = x' : t m bs where (x', m) = divMod x b
%o a235168_tabf = map a235168_row [0..]
%Y Cf. A002110, A049345, A108731, A235224 (row lengths), A276086.
%K nonn,tabf,base,look
%O 0,7
%A _Reinhard Zumkeller_, Jan 05 2014
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