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

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, 34, 36, 38, 40, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 77, 79

Offset: 0

Author

Amarnath Murthy, Jun 18 2002

Keywords

• base
• nonn

Examples

			a(1347) = 1 + 13 + 134 + 1347 + 347 + 47 + 7 = 1896.
		

Links

• Zak Seidov, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A225580. - Zak Seidov, May 16 2013

Programs

Maple

read("transforms"):
A071980 := proc(n)
    local a,dgs,d ;
    a := n ;
    dgs := convert(n,base,10) ;
    for d from 1 to nops(dgs) do
        [op(d+1..nops(dgs),dgs)] ;
        a := a+digcatL(%) ;
        [op(1..nops(dgs)-d,dgs)] ;
        a := a+digcatL(%) ;
    end do:
    a ;
end proc: # R. J. Mathar, May 06 2019

Mathematica

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}]
Table[n+Sum[Quotient[n,10^k]+Mod[n,10^k],{k,1,Log[10,n]}],{n,0,100}](* Zak Seidov, May 16 2013 *)

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))

Extensions

Edited by Robert G. Wilson v, Jun 23 2002