cp's OEIS Frontend

A276326 Numbers expressed in greedy A001563-base.

%I A276326 #29 Sep 01 2016 10:54:15
%S A276326 0,1,2,3,10,11,12,13,20,21,22,23,30,31,32,33,40,41,100,101,102,103,
%T A276326 110,111,112,113,120,121,122,123,130,131,132,133,140,141,200,201,202,
%U A276326 203,210,211,212,213,220,221,222,223,230,231,232,233,240,241,300,301,302,303,310,311,312,313,320,321,322,323,330,331,332,333,340,341,400
%N A276326 Numbers expressed in greedy A001563-base.
%C A276326 Terms A001563(1) = 1, A001563(2) = 4, A001563(3) = 18, ... give the base values for the digit positions from 1 onward. Digit places are filled by always trying to find the largest possible term of A001563 that still fits into the sum.
%C A276326 A130744(8) = 3225600 = 10*A001563(8) is the first number which yields an ambiguous representation when expressed in decimal, because in this base it is actually "A0000000" (where digit "A" stands for ten).
%H A276326 Antti Karttunen, <a href="/A276326/b276326.txt">Table of n, a(n) for n = 0..4320</a>
%e A276326 To recover n from a(n) the digits in positions i = 1, 2, 3, ... (starting indexing from the least significant digit at right) are multiplied by A001563(i) and added together:
%e A276326   ----------------
%e A276326    n         a(n)
%e A276326   ----------------
%e A276326    0           0
%e A276326    1           1
%e A276326    2           2
%e A276326    3           3
%e A276326    4          10
%e A276326    5          11
%e A276326    6          12
%e A276326    7          13
%e A276326    8          20
%e A276326    9          21
%e A276326   10          22
%e A276326   11          23
%e A276326   12          30
%e A276326   13          31
%e A276326   14          32
%e A276326   15          33
%e A276326   16          40
%e A276326   17          41 (as 4*A001563(2) + 1*A001563(1) = 17)
%e A276326   18         100 (as 1*A001563(3) + 0*A001563(2) + 0*A001563(1) = 18)
%e A276326 and:
%e A276326 3225599 99111111 (as 3225599 = 9*b(8) + 9*b(7) + b(6) + b(5) + b(4) + b(3) + b(2) + b(1)), where b(n) = A001563(n).
%t A276326 f[n_] := Block[{a = {{0, n}}}, Do[AppendTo[a, {First@ #, Last@ #} &@ QuotientRemainder[a[[-1, -1]], (# #!) &[# - i]]], {i, 0, # - 1}] &@ NestWhile[# + 1 &, 0, (# #!) &[# + 1] <= n &]; Rest[a][[All, 1]]]; Table[FromDigits@ f@ n, {n, 72}] (* _Michael De Vlieger_, Aug 31 2016 *)
%o A276326 (Scheme)
%o A276326 (define (A276326 n) (let loop ((n n) (s 0)) (if (zero? n) s (let ((dig (A276333 n))) (if (> dig 9) (error "A276326: ambiguous representation of n, digit > 9 would be needed: " n dig) (loop (A276335 n) (+ s (* dig (expt 10 (- (A258198 n) 1))))))))))
%Y A276326 Cf. A001563, A130744, A258198, A276335.
%Y A276326 Cf. A276327 (the least significant nonzero digit).
%Y A276326 Cf. A276328 (the sum of digits).
%Y A276326 Cf. A276333 (the most significant digit).
%Y A276326 Cf. A276336 (a largest digit).
%Y A276326 Cf. A276337 (number of nonzero digits).
%Y A276326 Cf. A033312 (repunits).
%Y A276326 Cf. A276091 (no digits larger than one).
%Y A276326 Differs from A007090 for the first time at n=16 and from A055655 at n=18.
%Y A276326 Cf. also A007623, A007961, A000433, A014418, A265747.
%K A276326 nonn,base
%O A276326 0,3
%A A276326 _Antti Karttunen_, Aug 30 2016