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

0,12

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A007953.

Sequence in context: A297236 A103693 A117230 * A138953 A307629 A053392

Adjacent sequences: A093879 A093880 A093881 * A093883 A093884 A093885

Keyword

base,nonn,look

Author

Amarnath Murthy, Apr 22 2004

Extensions

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

Offset corrected by Alois P. Heinz, May 06 2019

Status

approved