A198044 a(n) is the smallest number k such that d(1)*1! + d(2)*2! + ... + d(p)*p! = n, where d(1),...,d(p) are the decimal digits of k, or 0 if no such number exists.

1, 2, 3, 4, 5, 6, 7, 8, 9, 24, 15, 25, 16, 26, 17, 27, 18, 28, 19, 29, 39, 49, 59, 69, 79, 89, 99, 214, 124, 224, 105, 205, 115, 215, 125, 225, 106, 206, 116, 216, 126, 226, 107, 207, 117, 217, 127, 227, 108, 208, 118, 218, 128, 228, 109, 209, 119, 219, 129

Offset

1,2

Comments

If 9*A007489(d) < n < (d+1)! then a(n)=0. The least d for which 9*A007489(d)+1<(d+1)! is 10, so a(n)=0 for 36341217 < n < 39916800. - Robert Israel, Aug 16 2020

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(59) = 129 because 1*1! + 2*2! + 9*3! = 1+4+54 = 59.

Maple

for n from 1 to 70 do :i:=0:for nn from 1 to 1000 while(i=0) do:l:=length(nn):n0:=nn:s:=0:for m from l by -1  to 1 do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v :s:=s+u*m!:od: if s=n then i:=1:printf(`%d, `, nn):else fi:od:od:

Mathematica

Table[k = 1; While[d = IntegerDigits[k]; s = Sum[d[[i]] i!, {i, Length[d]}]; s != n, k++]; k, {n, 100}] (* T. D. Noe, Oct 20 2011 *)

Crossrefs

Cf. A007489.

Sequence in context: A307636 A048386 A302503 * A133134 A133505 A068407

Adjacent sequences: A198041 A198042 A198043 * A198045 A198046 A198047

Keyword

nonn,base,look

Author

Michel Lagneau, Oct 20 2011

Extensions

Definition edited by Robert Israel, Aug 16 2020

Status

approved