WebFeb 3, 2024 · Mathematical activities involving palindromic numbers. Palindromes A palindrome is a word, phrase, number or expression that reads the same backward as forward, e.g. Level, "Never odd or even", 12321 or x + 22 = 22 + x Here are some activities with a palindromic connection: Dates 3 — 2 — 23 4 — 2 — 24 5 — 2 — 25 6 — 2 — 26 … The palindromic square numbers are 0, 1, 4, 9, 121, 484, 676, 10201, 12321, ... (sequence A002779 in the OEIS ). It is obvious that in any base there are infinitely many palindromic numbers, since in any base the infinite sequence of numbers written (in that base) as 101, 1001, 10001, 100001, etc. consists … See more A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16461) that remains the same when its digits are reversed. In other words, it has reflectional symmetry across … See more All numbers in base 10 (and indeed in any base) with one digit are palindromic, so there are ten decimal palindromic numbers with one digit: See more If the digits of a natural number don't only have to be reversed in order, but also subtracted from $${\displaystyle b-1}$$ to yield the original sequence again, then the number is said to be antipalindromic. Formally, in the usual decomposition of a natural number into … See more The sum of the reciprocals of the palindromic numbers is a convergent series, whose value is approximately 3.37028... (sequence See more Although palindromic numbers are most often considered in the decimal system, the concept of palindromicity can be applied to the natural numbers in any numeral system. Consider a number n > 0 in base b ≥ 2, where it is written in standard notation with k+1 See more Palindromic numbers can be considered in numeral systems other than decimal. For example, the binary palindromic numbers are those with the … See more Non-palindromic numbers can be paired with palindromic ones via a series of operations. First, the non-palindromic number is reversed and the result is added to the original number. If the result is not a palindromic number, this is repeated until it gives a … See more

Palindromes - RecMath

WebPalindrome Word Squares. 2D Palindromes are word squares in which every row and column reads as a word in both directions: There are relatively few possible 2D palindromic squares. But if you allow names and obsolete words it is possible to make squares of not only 3x3 and 4x4, but also 5x5 and 6x6 size. Click here to see more 2D palindromic ... WebA palindrome is a number that reads the same backwards as forwards, such as 121, 363, 3883, 37973, to mention a few. Palindromic numbers can be prime, composite, odd, even, square, cube, and so on. The regular numbers, such as the examples just mentioned, are infinite in quantity. kitchen mobility occupational therapy

Palindromes that are sum of consecutive squares

WebMar 5, 2024 · A palindromic number is one that is the same when the digits are reversed, for example 18381. All numbers turn out to be palindromes in some number base. We look at sequences of Palindromes and find a surprisingly small number of palindromes are needed to make a sum for any given number (in a given base). WebNov 8, 2024 · Python can handle larger numbers, though the calculations will become slower, so you may actually find a palindrome. Here is a simple way to loop through just the square triangular numbers, skipping over 0 and 1 which are trivial. nold = 0 n = 1 for nm in infinity (2): nold, n = n, 34 * n - nold + 2 # check if n is a palindrome. WebThe following problems are studied: palindromic primes, palindromic squares and higher powers, multi-base palindromic numbers, etc. In this paper, we define and study antipalindromic numbers: positive integers … macbook pro putty