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.

1, 0, 12, 595968, 3909511, 0, 13177388, 1033, 10, 0, 0, 0, 0, 0, 77399307003, 1053202, 7413245658, 419370838921, 985992657240, 1347536041, 3216829919793, 1262490630568, 3606012949057, 5398293152472, 4119883235101, 0, 24006899084988, 405287637330, 15577274860798

Offset: 1

Author

Chai Wah Wu, Dec 06 2017

Keywords

• nonn
• base

Comments

a(n) = A236067(n) if and only if A296139(n) <= 1.

a(1000) = 1000000000001000003017, a(10000) = 0. - Chai Wah Wu, Dec 07 2017

Examples

			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).
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).
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A139410, A236067 (least such number), A296139 (number of solutions).

Programs

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