A068616 Starting from a(1)=7, each subsequent term is the minimal square obtained by inserting at least one digit into the previous term.

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

Offset

1,1

Links

Table of n, a(n) for n=1..13.

Index entries for linear recurrences with constant coefficients, signature (100).

Formula

For n>=5, a(n) = 1547536*100^(n-5).

From Chai Wah Wu, Aug 03 2020: (Start)

a(n) = 100*a(n-1) 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

Cf. A068175, A068176, A068177, A068178.

Sequence in context: A159029 A308582 A332157 * A080810 A153405 A322899

Adjacent sequences: A068613 A068614 A068615 * A068617 A068618 A068619

Keyword

base,nonn

Author

Amarnath Murthy, Feb 25 2002

Extensions

More terms from R. J. Mathar, Jun 26 2007

5 more terms from Sean A. Irvine, Sep 27 2009

Edited by Max Alekseyev, Oct 12 2009

Status

approved