A307629 - OEIS

%I #27 May 06 2019 08:53:46

%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 7,8,9,10,11,12,13,14,15,7,8,9,10,11,12,13,14,15,16,8,9,10,11,12,13,14,15,16,17,9,10,11,12,13,14,15,16,17,18,2,4,6

%N Let decimal expansion of n be d_1 d_2 ... d_k; a(n) = Sum_{i=1..k-1} Sum_{j=i+1..k} (d_i + d_j).

%C More than the usual number of terms are shown in order to distinguish this from related sequences.

%C Starts to differ from A093882 at A093882(101)=22 <> a(101)=4. - _R. J. Mathar_, May 06 2019

%H Michael De Vlieger, <a href="/A307629/b307629.txt">Table of n, a(n) for n = 0..10000</a>

%F From _Alois P. Heinz_, Apr 19 2019: (Start)

%F a(n) = A007953(n) * (A055642(n)-1).

%F a(n) = A110805(n) - A007953(n). (End)

%e For n<10 there is only one decimal digit so a(n)=0.

%e a(102) = 1+0 + 1+2 + 0+2 = 6.

%p a:= n-> (d-> (nops(d)-1)*add(i, i=d))(convert(n, base, 10)):

%p seq(a(n), n=0..120);  # _Alois P. Heinz_, Apr 19 2019

%t Array[Total@ Flatten@ Subsets[IntegerDigits@ #, {2}] &, 103, 0] (* _Michael De Vlieger_, Apr 19 2019 *)

%Y Cf. A007953, A055642, A110805, A138953.

%Y Suggested by A307560.

%K nonn,look,base

%O 0,12

%A _N. J. A. Sloane_, Apr 19 2019