Recent content by Janosh89

Please take down my post if it does not contribute to the thread

In #11 PeroK mentions finite series, as someone who has rudimentary maths & is recovering from a brain injury , I'm assuming these series converge to some value , π in the instance the OP alluded to. Infinite Series are treated in some other way [ eg 12x +1 which contains all the primes...

:smile:Welcome to PF from a fellow (retired) M.Engineer

I should have noticed :- for n=38 2(12*38+9)+1 is divisible by 7*19 . Does the pattern hold for the distinct prime factors , P4k+3 , of 2*(12n +9)+1 ?

I noticed that all my examples where 2*(12*n+9)+1 divides 2(12n+9)+1 were prime divisors. I will endeavor to find further counterexamples. Thanks .

It seems to hold true .. n factor(s) of (24n+19) (24n+19) divides 2(12n+9)+1 ? 0 19 YES 1 43 YES 2 67 YES 3 7, 13 NO 4 23, 5 NO 5 139 YES 6 163 YES 7 11, 17 NO 8 211 YES 9 47, 5 NO 10 7, 37 NO 11 283 YES

Apparently , the concept of negative energy exists . Perhaps , and only perhaps , this might be a prerequisite to the possibility of time travel.. In relation to #2 , various factors (unknown to me) would have to be knitted together.

Welcome to PF , shberry . .. from another PF Quark in UK ! o:) [ egg on face !???*]

Is it true that the Japanese Ambassador to Washington was unable to deliver the Declaration of War against the US in time before Pearl Harbor because of delays in decoding the said text sent from Tokyo ? My grandfather stayed behind in the Red Cross when Singapore fell . The British sappers...

x = 18 =33 ??! at approx 1.01 mins.

Welcome to PF , Parth Lawania :smile:

Yes , it was explicit.

I will post, y=x2+163 in future ##81^2+81+41=163×41## ##y=x^2+x+41## ##∴y=163×41~ when~x=81##

Nor me! ##\rm The~core~equation~for~~~##x2+x+41 ##\rm~~~~~~~~~~~~~~~is~~~~~~~~~~~~~~~~##x2+163 this will be divisible by 163 at n=81 of course, at n=40 , i.e. 40 x 41 [x1] ##~~~~~~~~~~~~## and n=41##~~~~~~~## 41 x 42 ##~~ "## the first composites ( of 41) are...

Of course , the Harmonic Series is "stand out " and the title - HS- it is given affords it the gravitas it deserves ; thus the fifth , sixth , seventh or whatever term is the 5th ... HARMONIC and so on .