A028553 Numbers k such that k*(k+3) is a palindrome.

0, 1, 8, 28, 66, 88, 211, 298, 671, 2126, 2998, 28814, 29369, 29998, 63701, 212206, 212671, 299998, 636776, 2122206, 2861419, 2999998, 9443423, 21341691, 28862883, 29999998, 212325206, 289053683, 294127328, 294174669, 299999998, 2134473706, 2946920844, 2999999998

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Comments

Also: numbers k such that the sum of the first k even composites is palindromic. Sequence is 4 + 6 + 8 + 10 + 12 + 14 + ... + z. For values of z see A058851. (Comment added by author 12/2000.)

All numbers of the form 3*10^j - 2 for j >= 0 are terms. For n > 1, a(n) mod 10 is one of {1,3,4,6,8,9}. - Chai Wah Wu, Feb 20 2021

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..40
• Patrick De Geest, Palindromic Quasipronics
• Patrick De Geest, Palindromic Sums 2
• Erich Friedman, What's Special About This Number? (See entries 298, 2126, 2998.)

Crossrefs

Cf. A058852, A028554.

Programs

Mathematica

(Sqrt[4#+9]-3)/2&/@Select[Table[k(k+3),{k,0,3*10^6}],PalindromeQ] (* The program generates the first 22 terms of the sequence. *) (* Harvey P. Dale, Oct 03 2023 *)

Python

n, m, A028553_list = 0, 0, []
while n < 10**12:
    s = str(m)
    if s == s[::-1]:
        A028553_list.append(n)
    m += 2*(n+2)
    n += 1 # Chai Wah Wu, Feb 20 2021

Extensions

More terms from Chai Wah Wu, Feb 20 2021