A246426 Number of steps in base n after which all digits > 0 are present in x(i) where x(i) = x(i-1) + sum of missing digits of x(i-1) with x(0) = 0.

1, 2, 12, 35, 266, 2486, 28781, 409929, 6824303, 130615525, 2846762052, 69481280019, 1875107560799, 55466043249309, 1791220240413582, 62561482660495103, 2351822439519905841, 94645194753881075173, 4053272062427790574310, 185031225489554592624010

Offset

2,2

Comments

Let x(i) = x(i-1) + A216407(x(i-1)), with x(0) = 0. a(n) is the smallest i such that A216407(x(i)) = 0.

Links

Table of n, a(n) for n=2..21.

Example

154 + missingdigit(154, 10) = 154 + 2+3+6+7+8+9 = 189.
The sequence looks like this in bases 2, 3 and 10:
0 + missingdigit(0,2) = 0 + 1 = 1.
missingdigit(1,2) = 0. (1 step)
0 + missingdigit(0,3) = 0 + (1+2) = 10.
10 + missingdigit(10,3) = 10 + 2 = 12.
missingdigit(12,3) = 0. (2 steps)
0 + missingdigit(0,10) = 0 + 45 = 45.
45 + missingdigit(45) = 45 + 36 = 81.
81 + missingdigit(81) = 81 + 36 = 117.
117 + missingdigit(117) = 117 + 37 = 154.
154 + missingdigit(154) = 154 + 35 = 189.
After 6824303 steps, the sequence reaches 123456978 and stops, because missingdigit(123456978) = 0.

Prog

(PARI) { bmx=12; for(b=2, bmx, n=0; miss=1; c=0; all=b*(b-1)/2; while(miss>0, d=vecsort(digits(n, b), , 8); miss=all-sum(i=1, #d, d[i]); n+=miss; c++; ); print1(c-1, ", "); ); }

Crossrefs

Cf. A216407.

Sequence in context: A334838 A200543 A363453 * A353503 A176583 A011379

Adjacent sequences: A246423 A246424 A246425 * A246427 A246428 A246429

Keyword

nonn,base

Author

Anthony Sand, Aug 26 2014

Extensions

a(13)-a(21) from Hiroaki Yamanouchi, Aug 02 2015

Status

approved