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

Author

Max Alekseyev, Jun 09 2018

Keywords

• base
• nonn

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.

Examples

			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