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
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.
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