A235400 a(1)=1. For n>1, assume a(n-1) has decimal expansion qrstuvwxyz (with at most ten digits, where some of q, r, s, ... may be zero). Then a(n) = sum 99...9 (with z 9's) + 88...8 (with y 8's) + 77...7 (with x 7's) + ... For example, if a(n-1) were 243, we would sum 77 + 8888 + 999 and get 9964.

1, 9, 999999999, 4999999995, 4000099995, 2888988885, 800099995, 2900099996, 3000999996, 3334333329, 1000006195, 889655560, 368199996, 2923444555, 111394795, 1452329335, 666792195, 1449655625, 334781195, 948992565, 1145513395, 889070335, 372323885, 168990195

Offset

1,2

Comments

The sequence is periodic: a(470) = a(312) = 8005, etc.

See A235460 for the analogous sequence where we number the digits starting with 1 at the leftmost digit.

References

Rodolfo Kurchan, Problems with repdigits, to appear in Proceedings of Gathering for Gardner 2014 conference

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Example

1 leads to one 9, then 9 leads to 999999999, then we have to sum 111111111 + 222222222 + ... + 999999999 = 4999999995, then we have to sum 1111 + 222222222 + ... + 888888888 + 99999 = 4000099995, and so on.

Mathematica

nxt[n_]:=Total[FromDigits/@(Table[#[[1]], {#[[2]]}]&/@Thread[{ Range[ 9, 10-IntegerLength[n], -1], Reverse[IntegerDigits[n]]}])]; NestList[ nxt, 1, 30] (* Harvey P. Dale, Apr 24 2015 *)

Crossrefs

Cf. A235460.

Sequence in context: A358814 A225775 A154110 * A028446 A058470 A058434

Adjacent sequences: A235397 A235398 A235399 * A235401 A235402 A235403

Keyword

nonn,base,nice

Author

Rodolfo Kurchan, Jan 09 2014

Status

approved