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A330633 The concatenation of the products of every pair of consecutive digits of n (with a(n) = 0 for 0 <= n <= 9).

%I A330633 #27 Apr 28 2020 14:58:05
%S A330633 0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,0,2,4,6,8,10,12,14,16,18,0,3,
%T A330633 6,9,12,15,18,21,24,27,0,4,8,12,16,20,24,28,32,36,0,5,10,15,20,25,30,
%U A330633 35,40,45,0,6,12,18,24,30,36,42,48,54,0,7,14,21,28,35,42,49,56,63,0
%N A330633 The concatenation of the products of every pair of consecutive digits of n (with a(n) = 0 for 0 <= n <= 9).
%C A330633 If the decimal expansion of n is d_1 d_2 ... d_k then a(n) is the number formed by concatenating the decimal numbers d_1*d_2, d_2*d_3, ..., d_{k-1}*d_k.
%C A330633 Due to the fact that for two digit numbers the sequence is simply the multiplication of those two numbers, this sequence matches numerous others for the first 100 terms. See the sequences in the cross references. The terms begin to differ beyond n = 100.
%H A330633 Scott R. Shannon, <a href="/A330633/b330633.txt">Table of n, a(n) for n = 1..10000</a>
%F A330633 a(10) = 0 as 1 * 0 = 0.
%F A330633 a(29) = 18 as 2 * 9 = 18.
%F A330633 a(100) = 0 as 1 * 0 = 0 and 0 = 0 = 0, and '00' is reduced to 0.
%F A330633 a(110) = 10 as 1 * 1 = 1 and 1 * 0 = 0. This is the first term that differs from A007954 and A171765, the multiplication of all digits of n.
%p A330633 read("transforms") :
%p A330633 A330633 := proc(n)
%p A330633     local dgs,L,i ;
%p A330633     if n <=9 then
%p A330633         0;
%p A330633     else
%p A330633         dgs := ListTools[Reverse](convert(n,base,10)) ;
%p A330633         L := [] ;
%p A330633         for i from 2 to nops(dgs) do
%p A330633             L := [op(L), op(i-1,dgs)*op(i,dgs)] ;
%p A330633         end do:
%p A330633         digcatL(L) ;
%p A330633     end if;
%p A330633 end proc: # _R. J. Mathar_, Jan 11 2020
%t A330633 Array[If[Or[# == 0, IntegerLength@ # == 1], 0, FromDigits[Join @@ IntegerDigits[Times @@ # & /@ Partition[IntegerDigits@ #, 2, 1]]]] &, 81, 0] (* _Michael De Vlieger_, Dec 23 2019 *)
%o A330633 (PARI) a(n) = my(d=digits(n), s="0"); for (k=1, #d-1, s=concat(s, d[k]*d[k+1])); eval(s); \\ _Michel Marcus_, Apr 28 2020
%Y A330633 Cf. A007954, A088117, A040115, A053392, A035930, A257850, A080464, A171765, A169669, A257297.
%K A330633 nonn,base,easy
%O A330633 0,13
%A A330633 _Scott R. Shannon_, Dec 21 2019