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A174525 Bases N in which ab and ba are different squares, for some a and b. 2
9, 12, 17, 19, 24, 25, 28, 33, 40, 49, 51, 52, 57, 60, 64, 67, 72, 73, 79, 81, 84, 88, 89, 96, 97, 99, 103, 105, 108, 112, 115, 116, 121, 124, 129, 134, 136, 144, 145, 148, 156, 161, 163, 168, 169, 172, 177, 180, 184, 192, 193, 199 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From Robert Israel, Mar 14 2016: (Start)

Leading 0's are not allowed.

Conjecture: all odd squares (A016754) except 1 are terms of the sequence. (End)

N=(2n+1)^2, a=n^2, b=4n^2+2n+1 shows that (2n+1)^2 is a term, so this sequence is infinite. - Michael R Peake, Mar 21 2017

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

17_9 and 71_9 are squares. 14_12 and 41_12 are squares.

MAPLE

filter:= proc(n) local x, a, b, R;

    for x from ceil(sqrt(n)) to n-1 do

      a:= x^2 mod n;

      if a=0 then next fi;

      b:= (x^2-a)/n;

      if assigned(R[b, a]) then return true fi;

      R[a, b]:= 1;

    od;

    false

end proc:

select(filter, [$1..1000]); # Robert Israel, Mar 14 2016

PROG

(MATLAB)

Match = zeros(1, 100);

for N=2:200, Tens=zeros(1, N-1); Units=zeros(1, N-1); for a=N-1:-1:sqrt(N), c=a^2; Tens(a)=floor(c/N); Units(a)=rem(c, N); end; for a=N-1:-1:sqrt(N), h=find((Units==Tens(a))&([1:N-1]~=a)); if length(h), Match=any(Units(a)==Tens(h)); if Match, Sol(N)=Sol(N)+1; end; end; end; end;

find(Match > 0)

CROSSREFS

Cf. A016754.

Sequence in context: A027571 A154631 A199593 * A141552 A317720 A162822

Adjacent sequences:  A174522 A174523 A174524 * A174526 A174527 A174528

KEYWORD

base,easy,nonn

AUTHOR

Michael R Peake, Mar 21 2010

EXTENSIONS

MATLAB program corrected by Robert Israel, Mar 14 2016

STATUS

approved

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Last modified October 22 14:44 EDT 2019. Contains 328318 sequences. (Running on oeis4.)