A276093 The least significant nonzero digit in primorial base is replaced with zero: a(n) = n - A276094(n), a(0) = 0.

0, 0, 0, 2, 0, 4, 0, 6, 6, 8, 6, 10, 0, 12, 12, 14, 12, 16, 0, 18, 18, 20, 18, 22, 0, 24, 24, 26, 24, 28, 0, 30, 30, 32, 30, 34, 30, 36, 36, 38, 36, 40, 30, 42, 42, 44, 42, 46, 30, 48, 48, 50, 48, 52, 30, 54, 54, 56, 54, 58, 0, 60, 60, 62, 60, 64, 60, 66, 66, 68, 66, 70, 60, 72, 72, 74, 72, 76, 60, 78, 78, 80, 78, 82, 60, 84, 84, 86, 84, 88, 0, 90

Offset: 0

Author

Antti Karttunen, Aug 22 2016

Keywords

• nonn
• base

Examples

			   n   A049345  with the rightmost      converted back
                nonzero replaced by 0   to decimal = a(n)
---------------------------------------------------------
   0       0             0                     0
   1       1             0                     0
   2      10            00                     0
   3      11            10                     2
   4      20            00                     0
   5      21            20                     4
   6     100           000                     0
   7     101           100                     6
   8     110           100                     6
   9     111           110                     8
  10     120           100                     6
  11     121           120                    10
  12     200           000                     0
  13     201           200                    12
  14     210           200                    12
  15     211           210                    14
  16     220           200                    12
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..2310
• Index entries for sequences related to primorial base

Crossrefs

Cf. A276094, A276086.

Programs

Mathematica

nn = 91; b = MixedRadix[Reverse@ Prime@ Range@ PrimePi[nn + 1]]; FromDigits[#, b] & /@ Join[{{0}}, Table[Function[w, Join[Take[w, Length@ w - # - 1], ConstantArray[0, # + 1]] &@ Length@ TakeWhile[Reverse@ w, # == 0 &]]@ IntegerDigits[n, b], {n, nn}]] (* Version 10.2, or *)
f[n_] := Block[{a = {{0, n}}}, Do[AppendTo[a, {First@ #, Last@ #} &@ QuotientRemainder[a[[-1, -1]], Times @@ Prime@ Range[# - i]]], {i, 0, #}] &@ NestWhile[# + 1 &, 0, Times @@ Prime@ Range[# + 1] <= n &]; Rest[a][[All, 1]]]; g[w_List] := Total[Times @@@ Transpose@ {Map[Times @@ # &, Prime@ Range@ Range[0, Length@ w - 1]], Reverse@ w}]; g /@ Join[{{0}}, Table[Function[w, Join[Take[w, Length@ w - # - 1], ConstantArray[0, # + 1]] &@ Length@ TakeWhile[Reverse@ w, # == 0 &]]@ f@ n, {n, 91}]] (* Michael De Vlieger, Aug 30 2016 *)

Scheme

(define (A276093 n) (- n (A276094 n)))

Formula

a(n) = n - A276094(n).