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A071980 If n = abcd (say) in decimal, then a(n) = a + ab + abc + abcd + bcd + cd + d.

%I A071980 #14 May 06 2019 08:28:22
%S A071980 0,1,2,3,4,5,6,7,8,9,11,13,15,17,19,21,23,25,27,29,22,24,26,28,30,32,
%T A071980 34,36,38,40,33,35,37,39,41,43,45,47,49,51,44,46,48,50,52,54,56,58,60,
%U A071980 62,55,57,59,61,63,65,67,69,71,73,66,68,70,72,74,76,78,80,82,84,77,79
%N A071980 If n = abcd (say) in decimal, then a(n) = a + ab + abc + abcd + bcd + cd + d.
%H A071980 Zak Seidov, <a href="/A071980/b071980.txt">Table of n, a(n) for n = 0..10000</a>
%e A071980 a(1347) = 1 + 13 + 134 + 1347 + 347 + 47 + 7 = 1896.
%p A071980 read("transforms"):
%p A071980 A071980 := proc(n)
%p A071980     local a,dgs,d ;
%p A071980     a := n ;
%p A071980     dgs := convert(n,base,10) ;
%p A071980     for d from 1 to nops(dgs) do
%p A071980         [op(d+1..nops(dgs),dgs)] ;
%p A071980         a := a+digcatL(%) ;
%p A071980         [op(1..nops(dgs)-d,dgs)] ;
%p A071980         a := a+digcatL(%) ;
%p A071980     end do:
%p A071980     a ;
%p A071980 end proc: # _R. J. Mathar_, May 06 2019
%t A071980 f[n_] := Block[{lead = IntegerDigits[n], trail = IntegerDigits[n], flr = Floor[Log[10, n] + 1], s = -n}, While[flr > 0, s = s + FromDigits[lead] + FromDigits[trail]; lead = Drop[lead, -1]; trail = Drop[trail, 1]; flr--]; s]; Table[f[n], {n, 0, 80}]
%t A071980 Table[n+Sum[Quotient[n,10^k]+Mod[n,10^k],{k,1,Log[10,n]}],{n,0,100}](* _Zak Seidov_, May 16 2013 *)
%o A071980 (PARI) a(n)=local(l); if(n<1,0,l=1+log(n)\log(10); sum(i=1,l-1,n\10^i+n%(10^i),n))
%Y A071980 Cf. A225580. - _Zak Seidov_, May 16 2013
%K A071980 base,nonn
%O A071980 0,3
%A A071980 _Amarnath Murthy_, Jun 18 2002
%E A071980 Edited by _Robert G. Wilson v_, Jun 23 2002