A305707 Numbers n such that for every k = 1, 2, ..., A305706(n)-1, it is possible to insert plus signs into the decimal representation of n^k to make sum equal n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 17, 45, 91, 100, 675, 945, 964, 990, 991, 1000, 1296, 1702, 2728, 4879, 5050, 5149, 5292, 7777, 8938, 9325, 9765, 9901, 9909, 9918, 9945, 9955, 9964, 10000, 10512, 12222, 12727, 17271, 41149, 42643, 48790, 50050, 59284, 72612, 75331, 77778, 81118, 87571, 93574, 95121, 99226, 99630, 99631, 99703, 99901, 99909, 99918, 99945, 99955, 99964, 99991, 100000, 104878, 117343, 329967, 461539

Offset

1,3

Comments

It is not possible to insert pluses in the decimal representation of n^A305706(n) to make the sum equal n.

Terms starting with a(15)=45 form a subsequence of A038206.

Links

Table of n, a(n) for n=1..73.

Example

For n = 45, we have A305706(n) = 6, and
n^1 = 45 with 45 = n;
n^2 = 2025 with 20+25 = n;
n^3 = 91125 with 9+11+25 = n;
n^4 = 4100625 with 4+10+0+6+25 = n;
n^5 = 184528125 with 18+4+5+2+8+1+2+5 = n.
So, 45 is a term.

Crossrefs

Cf. A038206, A305706

Sequence in context: A209860 A287513 A194403 * A161979 A247810 A247800

Adjacent sequences: A305704 A305705 A305706 * A305708 A305709 A305710

Keyword

base,nonn

Author

Max Alekseyev, Jun 09 2018

Status

approved