A263608 Palindromes which are base-3 representations of squares.

0, 1, 11, 121, 10201, 11111, 112211, 122221, 1002001, 1120211, 11022011, 100020001, 101212101, 122111221, 1012112101, 1100220011, 10000200001, 10111011101, 110002200011, 111221122111, 1000002000001, 1001221221001, 1012200022101, 1101202021011, 1221221221221, 10101111110101

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..143

G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]

Maple

rev3:= proc(n) local L, i; L:= convert(n, base, 3); add(L[-i]*3^(i-1), i=1..nops(L)) end proc:
c3:= proc(n) local L, i; L:= convert(n, base, 3); add(L[i]*10^(i-1), i=1..nops(L)) end proc:
R:= 0, 1: count:= 2:
for d from 2 while count < 100 do
    if d::odd then
      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)])
    else
      V:= select(issqr, [seq(a*3^(d/2) + rev3(a), a=3^(d/2-1) .. 3^(d/2)-1)]);
    fi;
    count:= count+nops(V);
    R:= R, op(map(c3, V));
od:
R; # Robert Israel, May 19 2024

Crossrefs

Cf. A002778, A003166, A029984, A262607, A029985.

Intersection of A001738 and A118594.

Sequence in context: A092846 A329734 A214993 * A088760 A080486 A342233

Adjacent sequences: A263605 A263606 A263607 * A263609 A263610 A263611

Keyword

nonn,base

Author

N. J. A. Sloane, Oct 22 2015

Extensions

Name edited by Robert Israel, May 19 2024

Status

approved