

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.


1



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



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



KEYWORD

base,nonn


AUTHOR



STATUS

approved



