

A093882


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


5



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
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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. AdamsWatters, 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..d1, 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[..i1],
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 *)


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. AdamsWatters, Jul 27 2006
Offset corrected by Alois P. Heinz, May 06 2019


STATUS

approved



