A108721 - OEIS

%I #4 May 25 2023 11:22:34

%S 111,133,205,315,515,845,1625,3460,6880,17600,35400,65600,138200,

%T 310600,547000,1160000,1980000,4480000,9920000,20180000,40220000,

%U 57940000,174380000,528780000,1964040000,5800840000,17533280000,64641960000

%N If a(n-1)=abcde..., where a,b,c,d,e... are the digits, then a(n)=abcde...+a*bcde...+ab*cde...+abc*de...+abcd*e...+....

%C The idea is from Peter Boros, borospet(AT)freemail.hu

%e a(5)=515, a(6)=515+5*15+51*5=515+75+255=845

%e a(7)=1625, a(8)=1625+1*625+16*25+162*5=1625+625+400+810=3460

%p a[1]:=111:for n from 2 to 40 do d:=a[n-1]:i:=1:while d>0 do c:=d mod 10:b[i]:=c:i:=i+1:d:=(d-c)/10 od:a[n]:=a[n-1]:for j from 1 to i-2 do f:=sum(b[k]*10^(k-1),k=1..j):g:=sum(b[k]*10^(k-j-1),k=j+1..i-1): a[n]:=a[n]+f*g od: od: seq(a[n],n=1..40);

%p # alternative

%p A108721 := proc(n)

%p     option remember ;

%p     local  a,dgs,ndgs,spl,fac1,fac2 ;

%p     if n = 1 then

%p         111;

%p     else

%p         a := procname(n-1) ;

%p         dgs := ListTools[Reverse](convert(a,base,10)) ;

%p         ndgs := nops(dgs) ;

%p         for spl from 1 to ndgs-1 do

%p             fac1 := [op(1..spl,dgs)] ;

%p             fac2 := [op(spl+1..ndgs,dgs)] ;

%p             a := a+digcatL(fac1)*digcatL(fac2) ; # digcatL defind in transforms

%p         end do:

%p         a ;

%p     end if;

%p end proc:

%p seq(A108721(n),n=1..70) ; # _R. J. Mathar_, May 25 2023

%K nonn,base

%O 1,1

%A _Miklos Kristof_, Jun 21 2005