cp's OEIS Frontend

A027723 Palindromes of form k^2 + k + 7.

%I A027723 #20 Aug 11 2024 14:41:29
%S A027723 7,9,313,999,31513,75357,78687,90909,98289,3159513,7642467,9009009,
%T A027723 743080347,900090009,31413131413,90000900009,97474147479,
%U A027723 3105075705013,9000009000009,757082131280757,900000090000009,907340818043709,90000000900000009,92269201110296229
%N A027723 Palindromes of form k^2 + k + 7.
%C A027723 From _Robert Israel_, May 16 2018: (Start)
%C A027723 Palindromes m such that 4*m - 27 is a square.
%C A027723 Each term has an odd number of digits and ends in 3, 7 or 9.
%C A027723 Contains 9*(1+10^k+10^(2*k)) for each k>=1. (End)
%H A027723 Giovanni Resta, <a href="/A027723/b027723.txt">Table of n, a(n) for n = 1..45</a>
%H A027723 P. De Geest, <a href="https://www.worldofnumbers.com/quasimor.htm">Palindromic Quasi_Over_Squares of the form n^2+(n+X)</a>
%p A027723 R[1]:= [1,3,5,7,9]: X[1]:= R[1]:
%p A027723 for k from 2 to 6 do
%p A027723   R[k]:= map(t -> seq(10^(k-1)*j+t,j=0..9),R[k-1]);
%p A027723 X[k]:= map(t -> seq(j+10*t,j=0..9),X[k-1])
%p A027723 od:
%p A027723 Res:= 7,9:
%p A027723 for k from 1 to 6 do
%p A027723   for j from 1 to 5*10^(k-1) do
%p A027723       r:= 10^(k+1)*X[k][j]+R[k][j];
%p A027723       for y from 0 to 9 do
%p A027723         if issqr(4*(r+10^k*y)-27) then
%p A027723           x:= r+10^k*y;
%p A027723           Res:= Res,x;
%p A027723         fi
%p A027723 od od od:
%p A027723 Res; # _Robert Israel_, May 16 2018
%Y A027723 Cf. A027722, A027692, A027756, A005471, A027721, A027725.
%K A027723 nonn,base
%O A027723 1,1
%A A027723 _Patrick De Geest_
%E A027723 More terms from _Giovanni Resta_, Aug 28 2018