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A108721
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...+....
1
111, 133, 205, 315, 515, 845, 1625, 3460, 6880, 17600, 35400, 65600, 138200, 310600, 547000, 1160000, 1980000, 4480000, 9920000, 20180000, 40220000, 57940000, 174380000, 528780000, 1964040000, 5800840000, 17533280000, 64641960000
OFFSET
1,1
COMMENTS
The idea is from Peter Boros, borospet(AT)freemail.hu
EXAMPLE
a(5)=515, a(6)=515+5*15+51*5=515+75+255=845
a(7)=1625, a(8)=1625+1*625+16*25+162*5=1625+625+400+810=3460
MAPLE
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);
# alternative
A108721 := proc(n)
option remember ;
local a, dgs, ndgs, spl, fac1, fac2 ;
if n = 1 then
111;
else
a := procname(n-1) ;
dgs := ListTools[Reverse](convert(a, base, 10)) ;
ndgs := nops(dgs) ;
for spl from 1 to ndgs-1 do
fac1 := [op(1..spl, dgs)] ;
fac2 := [op(spl+1..ndgs, dgs)] ;
a := a+digcatL(fac1)*digcatL(fac2) ; # digcatL defind in transforms
end do:
a ;
end if;
end proc:
seq(A108721(n), n=1..70) ; # R. J. Mathar, May 25 2023
CROSSREFS
Sequence in context: A279423 A213879 A095613 * A084325 A234803 A074253
KEYWORD
nonn,base
AUTHOR
Miklos Kristof, Jun 21 2005
STATUS
approved