A068657 Successive left concatenation of floor(k/2) beginning with n until we reach 1.

1, 21, 31, 421, 521, 631, 731, 8421, 9421, 10521, 11521, 12631, 13631, 14731, 15731, 168421, 178421, 189421, 199421, 2010521, 2110521, 2211521, 2311521, 2412631, 2512631, 2613631, 2713631, 2814731, 2914731, 3015731, 3115731, 32168421

Offset

1,2

Comments

Every a(j) will divide some a(k), j < k. - Robert G. Wilson v, Mar 02 2002

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

a(21) is constructed by starting with n, 21, then successively floor(21/2) = 10, floor(10/2) = 5, floor(5/2) = 2, floor(2/2) = 1, which is the end of the process of the halving. Now concatenate the results beginning with n: 21, 10, 5, 2, 1, which results in the number 2110521.

Maple

for m from 1 to 100 do a := m; n := m; while(n>1) do n := floor(n/2); if(n=1) then a := 10*a+1: else a := a*10^(ceil( log(n)/log(10)-0.000001) )+n:end if:end do:b[m] := a:end do:seq(b[i], i=1..100);

Mathematica

f[n_] := Floor[n/2]; Table[ ToExpression[ StringJoin[ ToString /@ Drop[ FixedPointList[f, n], -2]]], {n, 1, 35}]
Table[FromDigits[Flatten[IntegerDigits/@NestWhileList[Floor[#/2]&, n, #>1&]]], {n, 40}] (* Harvey P. Dale, Mar 09 2024 *)

Crossrefs

Sequence in context: A256824 A176558 A243360 * A068671 A166668 A019423

Adjacent sequences: A068654 A068655 A068656 * A068658 A068659 A068660

Keyword

base,easy,nonn

Author

Amarnath Murthy, Feb 28 2002

Extensions

More terms from Sascha Kurz, Mar 26 2002

Corrected by Robert G. Wilson v, Mar 02 2002

Status

approved