cp's OEIS Frontend

A296138 a(n) is the largest number m such that m = n^d_1 + n^d_2 + ... + n^d_k where d_k represents the k-th digit in the decimal expansion of m, or 0 if no such number exists.

%I A296138 #27 Jul 25 2025 11:40:10
%S A296138 1,0,12,595968,3909511,0,13177388,1033,10,0,0,0,0,0,77399307003,
%T A296138 1053202,7413245658,419370838921,985992657240,1347536041,
%U A296138 3216829919793,1262490630568,3606012949057,5398293152472,4119883235101,0,24006899084988,405287637330,15577274860798
%N A296138 a(n) is the largest number m such that m = n^d_1 + n^d_2 + ... + n^d_k where d_k represents the k-th digit in the decimal expansion of m, or 0 if no such number exists.
%C A296138 a(n) = A236067(n) if and only if A296139(n) <= 1.
%C A296138 a(1000) = 1000000000001000003017, a(10000) = 0. - _Chai Wah Wu_, Dec 07 2017
%H A296138 Chai Wah Wu, <a href="/A296138/b296138.txt">Table of n, a(n) for n = 1..500</a>
%e A296138 a(4) = 595968 since 595968 = 4^5 + 4^9 + 4^5 + 4^9 + 4^6 + 4^8 and it is the largest such number. It is different from A236067(4).
%e A296138 a(5) = 3909511 since 3909511 = 5^3 + 5^9 + 5^0 + 5^9 + 5^5 + 5^1 + 5^1 and it is the largest such number. It is the same as A236067(5).
%o A296138 (PARI) apply( {A296138(n)=my(m, N);while(n+m>10^m, m++); N=m; while(N*n^9>=10^N, N++); forstep(N=10^(N-!!N),10^m,-1, vecsum([n^d|d<-digits(N)])==N && return(N))}, [1..4]) \\ Naïve brute force; very slow for n > 4. - _M. F. Hasler_, Jul 24 2025
%Y A296138 Cf. A139410, A236067 (least such number), A296139 (number of solutions).
%K A296138 nonn,base
%O A296138 1,3
%A A296138 _Chai Wah Wu_, Dec 06 2017