Pre-previously on Overlord-of-the-Über-Feral, I looked at patterns like these, where sums of consecutive integers, sum(n1..n2), yield a number, n1n2, whose digits reproduce those of n1 and n2:

15 = sum(1..5)
27 = sum(2..7)
429 = sum(4..29)
1353 = sum(13..53)
1863 = sum(18..63)

Numbers like those can be called narcissistic, because in a sense they gaze back at themselves. Now I’ve looked at sums of consecutive reciprocals and found comparable narcissistic patterns:

0.45 = sum(1/4..1/5)
1.683... = sum(1/16..1/83)
0.361517... = sum(1/361..1/517)
3.61316... = sum(1/36..1/1316)
4.22847... = sum(1/42..1/2847)
3.177592... = sum(1/317..1/7592)
8.30288... = sum(1/8..1/30288)

Because the sum of consecutive reciprocals, 1/1 + 1/2 + 1/3 + 1/4…, is called the harmonic series, I’ve decided to call these numbers harcissistic = harmonic + narcissistic.

Post-Performative Post-Scriptum

Why did I put “Caveat Lector” (meaning “let the reader beware”) in the title of this post? Because it’s likely that some (or even most) fluent readers of English will misread the preceding word, “Harcissism”, as “Narcissism”.

Previously Pre-Posted (Please Peruse)

• Fair Pairs — looking at patterns like 1353 = sum(13..53)