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%I #22 Oct 27 2023 09:41:25
%S 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 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 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 Sum of all the numbers formed by deleting one digit from n.
%C 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 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 Alois P. Heinz, <a href="/A093882/b093882.txt">Table of n, a(n) for n = 0..20000</a>
%e a(123) = 12 + 13 + 23 = 48. [corrected by _Harvey P. Dale_, Jul 24 2017]
%p read("transforms"):
%p A093882 := proc(n)
%p local a,dgs,d,dgsred ;
%p a := 0 ;
%p dgs := convert(n,base,10) ;
%p for d from 1 to nops(dgs) do
%p [op(1..d-1,dgs),op(d+1..nops(dgs),dgs)] ;
%p a := a+digcatL(%) ;
%p end do:
%p a ;
%p end proc: # _R. J. Mathar_, May 06 2019
%p # second Maple program:
%p a:= n-> (s-> add(parse(cat("0", s[..i-1],
%p s[i+1..])), i=1..length(s)))(""||n):
%p seq(a(n), n=0..123); # _Alois P. Heinz_, May 06 2019
%t 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 (Python)
%o 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 print([a(n) for n in range(88)]) # _Michael S. Branicky_, Oct 27 2023
%Y Cf. A007953.
%K base,nonn,look
%O 0,12
%A _Amarnath Murthy_, Apr 22 2004
%E Corrected and extended by _Franklin T. Adams-Watters_, Jul 27 2006
%E Offset corrected by _Alois P. Heinz_, May 06 2019
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