

A068616


Starting from a(1)=7, each subsequent term is the minimal square obtained by inserting at least one digit into the previous term.


1



7, 576, 5476, 54756, 1547536, 154753600, 15475360000, 1547536000000, 154753600000000, 15475360000000000, 1547536000000000000, 154753600000000000000, 15475360000000000000000
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OFFSET

1,1


LINKS



FORMULA

For n>=5, a(n) = 1547536*100^(n5).
a(n) = 100*a(n1) for n > 5.
G.f.: x*(3928064*x^4 + 492844*x^3 + 52124*x^2 + 124*x  7)/(100*x  1). (End)


EXAMPLE

a(2)=576 hence a(3) = 5476 the smallest square formed from 576.


MAPLE

Digits := 30 : isContain := proc(n, k) local ndigs, kdigs, f, d ; ndigs := convert(n, base, 10) ; kdigs := convert(k, base, 10) ; f := 1 : for d from 1 to nops(ndigs) do if f > nops(kdigs) then RETURN(false) ; fi ; while op(f, kdigs) <> op(d, ndigs) do f := f+1 ; if f > nops(kdigs) then RETURN(false) ; fi ; od: f := f+1 ; od: RETURN(true) ; end: n := 7 ; s := 8 : while true do while not isContain(n, s^2) do s := s+1 : od ; print(s^2) ; n := s^2: s := ceil(sqrt(s^2+1)) : od: # R. J. Mathar, Jun 26 2007


CROSSREFS



KEYWORD

base,nonn


AUTHOR



EXTENSIONS



STATUS

approved



