A198044 - OEIS

%I #17 May 26 2024 19:18:01

%S 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,

%T 99,214,124,224,105,205,115,215,125,225,106,206,116,216,126,226,107,

%U 207,117,217,127,227,108,208,118,218,128,228,109,209,119,219,129

%N 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.

%C 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

%H Robert Israel, <a href="/A198044/b198044.txt">Table of n, a(n) for n = 1..10000</a>

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

%p 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:

%t 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 *)

%t snk[n_]:=Module[{k=1},While[Total[IntegerDigits[k]*Range[IntegerLength[k]]!]!=n,k++];k]; Array[ snk,60] (* _Harvey P. Dale_, May 26 2024 *)

%Y Cf. A007489.

%K nonn,base,look

%O 1,2

%A _Michel Lagneau_, Oct 20 2011

%E Definition edited by _Robert Israel_, Aug 16 2020