cp's OEIS Frontend

A093882 Sum of all the numbers formed by deleting one digit from n.

%I A093882 #22 Oct 27 2023 09:41:25
%S A093882 0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,10,2,3,4,5,6,7,8,9,10,11,3,4,5,
%T A093882 6,7,8,9,10,11,12,4,5,6,7,8,9,10,11,12,13,5,6,7,8,9,10,11,12,13,14,6,
%U A093882 7,8,9,10,11,12,13,14,15,7,8,9,10,11,12,13,14,15,16,8,9,10,11,12,13,14,15
%N A093882 Sum of all the numbers formed by deleting one digit from n.
%C A093882 Subsidiary sequence: Sum of the numbers formed by deleting all possible strings touching one end ( containing at least one of the LSB or MSB). A071980(123) = 123 + 12 + 1 + 23 + 3 = 162. A071980(1234) = 1 + 12 + 123 + 1234 + 234 + 34 + 4 = 1642.
%C A093882 This allows leading zeros are after deletion. If these are forbidden, the first change would be a(101) = 21 instead of 22. - _Franklin T. Adams-Watters_, Jul 27 2006
%H A093882 Alois P. Heinz, <a href="/A093882/b093882.txt">Table of n, a(n) for n = 0..20000</a>
%e A093882 a(123) = 12 + 13 + 23 = 48. [corrected by _Harvey P. Dale_, Jul 24 2017]
%p A093882 read("transforms"):
%p A093882 A093882 := proc(n)
%p A093882     local a,dgs,d,dgsred ;
%p A093882     a := 0 ;
%p A093882     dgs := convert(n,base,10) ;
%p A093882     for d from 1 to nops(dgs) do
%p A093882         [op(1..d-1,dgs),op(d+1..nops(dgs),dgs)] ;
%p A093882         a := a+digcatL(%) ;
%p A093882     end do:
%p A093882     a ;
%p A093882 end proc: # _R. J. Mathar_, May 06 2019
%p A093882 # second Maple program:
%p A093882 a:= n-> (s-> add(parse(cat("0", s[..i-1],
%p A093882          s[i+1..])), i=1..length(s)))(""||n):
%p A093882 seq(a(n), n=0..123);  # _Alois P. Heinz_, May 06 2019
%t A093882 sn[n_]:=Module[{idn=IntegerDigits[n]},Total[FromDigits/@Table[ Delete[ idn,i],{i,Length[idn]}]]]; Array[sn,90,0] (* _Harvey P. Dale_, Jul 24 2017 *)
%o A093882 (Python)
%o A093882 def a(n): s=str(n); return sum(int(s[:i]+s[i+1:]) for i in range(len(s))) if n > 9 else 0
%o A093882 print([a(n) for n in range(88)]) # _Michael S. Branicky_, Oct 27 2023
%Y A093882 Cf. A007953.
%K A093882 base,nonn,look
%O A093882 0,12
%A A093882 _Amarnath Murthy_, Apr 22 2004
%E A093882 Corrected and extended by _Franklin T. Adams-Watters_, Jul 27 2006
%E A093882 Offset corrected by _Alois P. Heinz_, May 06 2019