A305669 Take the sum of the digits of a number, put it at the left side and delete the same number of digits at the right side. Repeat the process. Sequence lists numbers that reach themselves after some steps.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 14, 17, 21, 32, 41, 51, 53, 54, 65, 81, 85, 95, 98, 101, 108, 109, 116, 171, 179, 210, 321, 632, 811, 910, 917, 1013, 1071, 1112, 1113, 1114, 1116, 1271, 1291, 1312, 1313, 1315, 1316, 1323, 1375, 1381, 1415, 1516, 1517, 1585

Offset

0,3

Comments

Fixed points of the process (numbers that reach themselves in a single step) are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1818, 17171, 272727, 1313131, 2626262, 3939393, 12121212, 24242424, 36363636, 48484848, etc.

The number of steps to return to the original number or to enter another cycle depends on the number of digits. Here below all possible steps against the number of digits from 1 to 8:

Digits Steps

1 1

2 3, 12

3 3, 9

4 1, 3, 10, 31

5 1, 9

6 1, 4, 13, 21, 39

7 1, 2, 4, 5, 6, 10, 12, 20, 23, 30, 60

8 1, 3, 26, 78

Links

Table of n, a(n) for n=0..55.

Maple

P:=proc(q) local a, b, c, d, k, n, x;
for n from 1 to q do a:=convert(n, base, 10); d:=a; x:=0;
while x<10^(ilog10(n)+1) do x:=x+1; b:=convert(a, `+`);
c:=ilog10(b)+1; b:=convert(b, base, 10);
for k from 1 to nops(a)-c do a[k]:=a[k+c]; od;
for k from 1 to c do a[nops(a)-c+k]:=b[k]; od;
if a=d then print(n); break; fi; od; od; end: P(10^6);

Crossrefs

Cf. A007953.

Sequence in context: A318736 A050741 A285710 * A325364 A133810 A176615

Adjacent sequences: A305666 A305667 A305668 * A305670 A305671 A305672

Keyword

nonn,easy,base

Author

Paolo P. Lava, Jun 19 2018

Status

approved