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A027723 Palindromes of form k^2 + k + 7. 4

%I #19 Aug 30 2018 02:56:37

%S 7,9,313,999,31513,75357,78687,90909,98289,3159513,7642467,9009009,

%T 743080347,900090009,31413131413,90000900009,97474147479,

%U 3105075705013,9000009000009,757082131280757,900000090000009,907340818043709,90000000900000009,92269201110296229

%N Palindromes of form k^2 + k + 7.

%C From _Robert Israel_, May 16 2018: (Start)

%C Palindromes m such that 4*m - 27 is a square.

%C Each term has an odd number of digits and ends in 3, 7 or 9.

%C Contains 9*(1+10^k+10^(2*k)) for each k>=1. (End)

%H Giovanni Resta, <a href="/A027723/b027723.txt">Table of n, a(n) for n = 1..45</a>

%H P. De Geest, <a href="http://www.worldofnumbers.com/quasimor.htm">Palindromic Quasi_Over_Squares of the form n^2+(n+X)</a>

%p R[1]:= [1,3,5,7,9]: X[1]:= R[1]:

%p for k from 2 to 6 do

%p R[k]:= map(t -> seq(10^(k-1)*j+t,j=0..9),R[k-1]);

%p X[k]:= map(t -> seq(j+10*t,j=0..9),X[k-1])

%p od:

%p Res:= 7,9:

%p for k from 1 to 6 do

%p for j from 1 to 5*10^(k-1) do

%p r:= 10^(k+1)*X[k][j]+R[k][j];

%p for y from 0 to 9 do

%p if issqr(4*(r+10^k*y)-27) then

%p x:= r+10^k*y;

%p Res:= Res,x;

%p fi

%p od od od:

%p Res; # _Robert Israel_, May 16 2018

%Y Cf. A027722, A027692, A027756, A005471, A027721, A027725.

%K nonn,base

%O 1,1

%A _Patrick De Geest_

%E More terms from _Giovanni Resta_, Aug 28 2018

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)