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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

%I #9 Jun 12 2018 10:14:15

%S 0,1,2,3,4,5,6,7,8,9,10,13,14,17,45,91,100,675,945,964,990,991,1000,

%T 1296,1702,2728,4879,5050,5149,5292,7777,8938,9325,9765,9901,9909,

%U 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

%N 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.

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

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

%e For n = 45, we have A305706(n) = 6, and

%e n^1 = 45 with 45 = n;

%e n^2 = 2025 with 20+25 = n;

%e n^3 = 91125 with 9+11+25 = n;

%e n^4 = 4100625 with 4+10+0+6+25 = n;

%e n^5 = 184528125 with 18+4+5+2+8+1+2+5 = n.

%e So, 45 is a term.

%Y Cf. A038206, A305706

%K base,nonn

%O 1,3

%A _Max Alekseyev_, Jun 09 2018

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)