Fifty is a peculiar integer.
When looking at its neighbors — the largest integer strictly beneath and the smallest strictly above –, more specifically their prime factorization, one finds

49=\underbrace{7^2<50<3\cdot 17}_{7+7+3=17}=51,

notably there exists a partition of the neighbor’s factors into two multisets such that both parts’ sums equal another.

Positive integers with the above described property can be found in my most recent addition to the OEIS: sequence A325902.


The On-Line Encyclopedia of Integer Sequences (also known by its acronym, OEIS) is a database hosting hundreds of thousands of — as the name implies — integer sequences. Yet, despite the massive number of entries, I contributed a new integer sequence, A278328.

A278328 describes numbers whose absolute difference to their decimal reverse are square. An example would be 12 or 21 (both are the decimal reverse to each other), since \left|12-21\right|=9 and 9=3^2.

Not a whole lot is known about the sequence, partly due to its definition only resulting in the sequence when using the decimal system, though it is known that there are infinitely many numbers with said property. Since there are infinitely many palindromes (numbers whose reverse is the number itself), \left|n-n\right|=0 and 0=0^2.

Due to there — to my knowledge — not being a direct formula for those numbers, I wrote a Python script to generate them. On the sequence’s page, I posted a program which endlessly spews them out, though I later wrote a Python two-liner, which only calculates those members of the sequence in the range from 0 to 98 (shown below entered in a Python shell).

>>> import math
>>> filter(lambda n:math.sqrt(abs(n-int(str(n)[::-1])))%1 == 0, range(99))
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 21, 22, 23, 26, 32, 33, 34, 37, 40, 43, 44, 45, 48, 51, 54, 55, 56, 59, 62, 65, 66, 67, 73, 76, 77, 78, 84, 87, 88, 89, 90, 95, 98]


This game is a recreation of the famous game Simon. In the game there are four colors which form a sequence that is expanding every cycle. The aim of the game is to memorize said sequence as far as possible.
For more information on the Simon game visit this Wikipedia entry.


  • Click on the colored buttons to press them

The first example The second example The third example

# Python 2.7.7 Code
# Pygame 1.9.1 (for Python 2.7.7)
# Jonathan Frech 24th of June, 2016

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