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Palindromes of form n^2 + (n+1)^2.
2

%I #21 Jan 19 2025 18:04:27

%S 1,5,181,313,545,1690961,3162613,3187813,5258525,5824285,58281418285,

%T 1635446445361,3166046406613,124852060258421,149988757889941,

%U 310433303334013,582818040818285,12951570707515921,5227371841481737225,5649436330336349465,5816694029204966185

%N Palindromes of form n^2 + (n+1)^2.

%C a(50) > 10^40. - _Patrick De Geest_, May 25 2021

%H Patrick De Geest, <a href="/A027572/b027572.txt">Table of n, a(n) for n = 1..49</a>

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/sumsquare.htm">Palindromic Sums of Squares of Consecutive Integers</a>

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/centered.htm">Palindromic Centered Polygonal Numbers</a>

%F a(n) = (4*m^2 - 4*m + 2)/2 = (m-1)^2 + m^2 or a(n) = (4*n^2 + 4*n + 2)/2 = n^2 + (n+1)^2 with n = m - 1.

%t Select[Total/@Partition[Range[0,2000]^2,2,1],PalindromeQ] (* The program generates the first 10 terms of the sequence. *) (* _Harvey P. Dale_, Jan 19 2025 *)

%Y Cf. A001844, A027571, A050236, A050239.

%Y A050239 is a subsequence.

%K nonn,base

%O 1,2

%A _Patrick De Geest_

%E a(18)-a(21) from _Donovan Johnson_, Aug 26 2012

%E a(1)=1 added by _Philip Mizzi_, Sep 02 2019

%E a(22)-a(49) from _Patrick De Geest_, May 25 2021