A305707 - OEIS

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

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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;