A027572 Palindromes of form n^2 + (n+1)^2.

1, 5, 181, 313, 545, 1690961, 3162613, 3187813, 5258525, 5824285, 58281418285, 1635446445361, 3166046406613, 124852060258421, 149988757889941, 310433303334013, 582818040818285, 12951570707515921, 5227371841481737225, 5649436330336349465, 5816694029204966185

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Comments

a(50) > 10^40. - Patrick De Geest, May 25 2021

Links

• Patrick De Geest, Table of n, a(n) for n = 1..49
• Patrick De Geest, Palindromic Sums of Squares of Consecutive Integers
• Patrick De Geest, Palindromic Centered Polygonal Numbers

Crossrefs

Cf. A001844, A027571, A050236, A050239.

A050239 is a subsequence.

Programs

Mathematica

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 *)

Formula

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.

Extensions

a(18)-a(21) from Donovan Johnson, Aug 26 2012

a(1)=1 added by Philip Mizzi, Sep 02 2019

a(22)-a(49) from Patrick De Geest, May 25 2021