cp's OEIS Frontend

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.

%I A305707 #9 Jun 12 2018 10:14:15
%S A305707 0,1,2,3,4,5,6,7,8,9,10,13,14,17,45,91,100,675,945,964,990,991,1000,
%T A305707 1296,1702,2728,4879,5050,5149,5292,7777,8938,9325,9765,9901,9909,
%U A305707 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 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.
%C A305707 It is not possible to insert pluses in the decimal representation of n^A305706(n) to make the sum equal n.
%C A305707 Terms starting with a(15)=45 form a subsequence of A038206.
%e A305707 For n = 45, we have A305706(n) = 6, and
%e A305707 n^1 = 45 with 45 = n;
%e A305707 n^2 = 2025 with 20+25 = n;
%e A305707 n^3 = 91125 with 9+11+25 = n;
%e A305707 n^4 = 4100625 with 4+10+0+6+25 = n;
%e A305707 n^5 = 184528125 with 18+4+5+2+8+1+2+5 = n.
%e A305707 So, 45 is a term.
%Y A305707 Cf. A038206, A305706
%K A305707 base,nonn
%O A305707 1,3
%A A305707 _Max Alekseyev_, Jun 09 2018