A027580 Palindromes of the form n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2.

55, 51015, 554455, 51488415, 510151015, 55883648705050784638855, 531578379527444725973875135

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base
• more

Comments

Terms start and end with the digit 5 since all terms are divisible by 5, i.e., the corresponding values of n are odd (see A027579). - Chai Wah Wu, Jan 18 2016

Links

• P. De Geest, Palindromic Sums of Squares of Consecutive Integers

Crossrefs

Cf. A027579.

Programs

Mathematica

Select[Table[n^2 + (n + 1)^2 + (n + 2)^2 + (n + 3)^2 + (n + 4)^2, {n, 10^7}], # == Reverse@ # &@ IntegerDigits@ # &] (* Michael De Vlieger, Jan 24 2016 *)
Select[Table[5x^2+20x+30,{x,11000}],PalindromeQ] (* The program generates the first 5 terms of the sequence. To generate more, increase the x constant but the program may take a long time to run. *) (* Harvey P. Dale, Sep 16 2023 *)

Python

A027580_list = []
for i in range(1,10**8,2):
    s = str(5*(i*(i+4)+6))
    if s == s[::-1]:
        A027580_list.append(int(s)) # Chai Wah Wu, Jan 18 2016

Extensions

a(6) from Chai Wah Wu, Jan 18 2016

a(7) from Giovanni Resta, Aug 04 2019