A156230 Sum of the products of the digits of n and the positions of the digits m in n starting from the last digit.

1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 3

Offset: 1

Author

Cino Hilliard, Feb 06 2009

Keywords

• base
• nonn

Comments

Starts to differ from A081594 when n>=100. [From R. J. Mathar, Feb 19 2009]

Examples

			a(19) = 9*1 + 1*2 = 11.
		

Programs

Maple

A156230 := proc(n)
    local dgs;
    dgs := convert(n,base,10) ;
    add(i*op(i,dgs),i=1..nops(dgs)) ;
end proc:
seq(A156230(n),n=1..100) ; # R. J. Mathar, Dec 02 2018

Mathematica

pdn[n_]:=Module[{idn=IntegerDigits[n]},Total[idn Range[Length[idn],1,-1]]]; Array[pdn,80] (* Harvey P. Dale, Aug 22 2012 *)

PARI

gr(n) = v=Vec((rev(n)));sum(x=1,length(v),x*eval(v[x]))
gr1(n) = for(j=1,n,print1(gr(j)","))
rev(str) = /* Get the reverse of the input string
*/ {
local(tmp,s,j);
tmp = Vec(Str(str));
s="";
forstep(j=length(tmp),1,-1,
s=concat(s,tmp[j]));
return(s)
}

Formula

Let n = d(1)d(2)...d(m) where d(1),d(2),...,d(m) are the digits of n. Then a(n) = m*d1+(m-1)*d2+...+d(m).

Extensions

Changed the description, formula and Pari code Cino Hilliard, Feb 08 2009

More terms to separate from A322001. - R. J. Mathar, Dec 02 2018