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

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, 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, 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

Offset: 0

Author

Amarnath Murthy, Apr 22 2004

Keywords

• base
• nonn
• look

Comments

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.

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

Examples

			a(123) = 12 + 13 + 23 = 48. [corrected by _Harvey P. Dale_, Jul 24 2017]
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..20000

Crossrefs

Cf. A007953.

Programs

Maple

read("transforms"):
A093882 := proc(n)
    local a,dgs,d,dgsred ;
    a := 0 ;
    dgs := convert(n,base,10) ;
    for d from 1 to nops(dgs) do
        [op(1..d-1,dgs),op(d+1..nops(dgs),dgs)] ;
        a := a+digcatL(%) ;
    end do:
    a ;
end proc: # R. J. Mathar, May 06 2019
# second Maple program:
a:= n-> (s-> add(parse(cat("0", s[..i-1],
         s[i+1..])), i=1..length(s)))(""||n):
seq(a(n), n=0..123);  # Alois P. Heinz, May 06 2019

Mathematica

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 *)

Python

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
print([a(n) for n in range(88)]) # Michael S. Branicky, Oct 27 2023

Extensions

Corrected and extended by Franklin T. Adams-Watters, Jul 27 2006

Offset corrected by Alois P. Heinz, May 06 2019