Hi Maple community, and all,
an arbitrary arithmetic progression, with starting value , s, 

and increasing by "a", where "a" is the value to add, every time,
so
{Arithmetic Progression} is found by calculating
s+a*index

where index is a running index 
see attached
arithmetic_progression_with_1_and_8.mw

arithmetic_progression_with_1_and_8.mw

hopefully, that is useful, as an example, of an arithmetic progression.

Regards,
Matt

Hi Maple community and others,

I'm very proud to present my code.

Sequences are fun,
for those who know, about them

consider Fermat numbers, of the form,
F(n) = (2^(2^n)) + 1.
goes like

3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, 
340282366920938463463374607431768211457, ...

in oeis.org database at
https://oeis.org/A000215 .

Similarly we can have base 3,

B(a) = (3^(3^a)) + 1.
goes like, this,
4,28,19684, ...
online, in database, with Universal Resource Location (URL)
https://oeis.org/A129290

There could also be base 4, that grows even faster
 

double_exponential_2_and_3_and_4.mw

That is all that I have, for now.

Thank you for this free forum.
regards,
Matt

Hi Maple community, and all,

Here is a little Maple worksheet, shoing an interesting property of prime numbers.

Numerical evidence supports Andreca's conjecture.

see    

_Andricas_conjecture.mw

good fun

see, also
Andrica's Conjecture -- from Wolfram MathWorld
Enjoy
regards,
Matt

PS online at https://MattAnderson.fun/

PPS Have a good day, everybody.

Hi MaplePrimes, and all,

Here is a new, to me, set of numbers
defined by ,
the first three numbers are {1,2,3}
and then, 
the next number is the sum of the three 
previous numbers,
so,
{1,2,3,6,11,20, ... }
but can only calculate a finite number of numbers
the, so called, Tribonacci numbers
could start with {0,1,0}
see online
https://oeis.org/A001590

and
triple_recursive_sequence_simple_first.mw

triple_recursive_sequence_simple_first.pdf

regards,
Matt
 

Hi again Maple community, and others,

want to share
tiwn_and_cousin_prime_numbers.mw
tiwn_and_cousin_prime_numbers.pdf
(spelling error in file name)

~

just want to share,
some successful code

The lesser of the twin primes are listed
{3,5,11,17,29,41,59,71}
https://oeis.org/A001359
Prime numbers p such that p+2 is also a prime number

also, the lesser of the cousin primes are listed
{3,7,13,19,37,43,67,79,97}
https://oeis.org/A023200
prime numbers p such that p+4 is also a prime number

good fun

also, my webpage has more details
https://mattanderson.fun
okay

regards,
Matt