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

1,3

Comments

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

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

Links

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

Example

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).

Prog

(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

Crossrefs

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

Sequence in context: A013796 A055312 A365242 * A350542 A159951 A283627

Adjacent sequences: A296135 A296136 A296137 * A296139 A296140 A296141

Keyword

nonn,base

Author

Chai Wah Wu, Dec 06 2017

Status

approved