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

1,2

Comments

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

Links

Table of n, a(n) for n=1..100.

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).

Example

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

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 *)

Prog

(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)
}

Crossrefs

Sequence in context: A173529 A273005 A093017 * A028897 A244158 A322001

Adjacent sequences: A156227 A156228 A156229 * A156231 A156232 A156233

Keyword

base,nonn

Author

Cino Hilliard, Feb 06 2009

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

Status

approved