A198095 a(n) is the smallest number k such that d(1)*1! + d(2)*2! + ... + d(p)*p! = n^2, where d(i) are the decimal digits of k.

1, 4, 9, 27, 79, 225, 108, 249, 999, 2104, 1005, 2235, 1007, 2108, 1119, 2169, 1999, 22132, 10003, 21213, 11133, 21004, 10024, 22334, 10015, 21035, 11106, 21226, 10007, 22127, 10008, 21228, 11109, 21039, 10069, 22389, 19999, 210002, 111302, 212112, 100022

Offset

1,2

Links

Table of n, a(n) for n=1..41.

Example

a(5) = 79 because 7*1! + 9*2! = 5^2.

Mathematica

Table[k = 1; While[d = IntegerDigits[k]; s = Sum[d[[i]] i!, {i, Length[d]}]; s != n^2, k++]; k, {n, 42}] (* after T. D. Noe, see A198044 *)

Prog

(PARI) f(n) = my(d=digits(n)); sum(k=1, #d, d[k]*k!);
a(n) = my(k=1); while (f(k) != n^2, k++); k; \\ Michel Marcus, Jul 11 2021

Crossrefs

Subsequence of A198044.

Sequence in context: A111962 A307528 A365609 * A256096 A071913 A007872

Adjacent sequences: A198092 A198093 A198094 * A198096 A198097 A198098

Keyword

nonn,base

Author

Michel Lagneau, Oct 21 2011

Status

approved