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A263608 Palindromes which are base-3 representations of squares.

%I A263608 #21 May 20 2024 10:16:37
%S A263608 0,1,11,121,10201,11111,112211,122221,1002001,1120211,11022011,
%T A263608 100020001,101212101,122111221,1012112101,1100220011,10000200001,
%U A263608 10111011101,110002200011,111221122111,1000002000001,1001221221001,1012200022101,1101202021011,1221221221221,10101111110101
%N A263608 Palindromes which are base-3 representations of squares.
%H A263608 Robert Israel, <a href="/A263608/b263608.txt">Table of n, a(n) for n = 1..143</a>
%H A263608 G. J. Simmons, <a href="/A002778/a002778.pdf">On palindromic squares of non-palindromic numbers</a>, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]
%p A263608 rev3:= proc(n) local L,i; L:= convert(n,base,3); add(L[-i]*3^(i-1),i=1..nops(L)) end proc:
%p A263608 c3:= proc(n) local L,i; L:= convert(n,base,3); add(L[i]*10^(i-1),i=1..nops(L)) end proc:
%p A263608 R:= 0,1: count:= 2:
%p A263608 for d from 2 while count < 100 do
%p A263608     if d::odd then
%p A263608       V:= select(issqr, [seq(seq(a*3^((d+1)/2) + b*3^((d-1)/2)+rev3(a),b=0..2),a=3^((d-3)/2) .. 3^((d-1)/2)-1)])
%p A263608     else
%p A263608       V:= select(issqr, [seq(a*3^(d/2) + rev3(a), a=3^(d/2-1) .. 3^(d/2)-1)]);
%p A263608     fi;
%p A263608     count:= count+nops(V);
%p A263608     R:= R, op(map(c3,V));
%p A263608 od:
%p A263608 R; # _Robert Israel_, May 19 2024
%Y A263608 Cf. A002778, A003166, A029984, A262607, A029985.
%Y A263608 Intersection of A001738 and A118594.
%K A263608 nonn,base
%O A263608 1,3
%A A263608 _N. J. A. Sloane_, Oct 22 2015
%E A263608 Name edited by _Robert Israel_, May 19 2024