Problems & Puzzles: Puzzles

Puzzle 1201 Two new curious functions

On Dec 11, 2024 Davide Rotondo wrote:

Here are two new and curious functions:

1) ceil((1.5)*n^2-72*n+879),n=>0

2) ceil((1.5)*n^2 + 15), n=>0

Both " for n even you get interprimes of cousin primes while for n odd you get primes".

The first equation produces 25 successive integers with the mentioned property. From 25 on it produces the same values in reverse order"

The second equation makes the same but for 26 successive values.

Results:

ceil((1.5)*n^2-72*n+879),n=>0 ceil((1.5)*n^2 + 15), n=>0
n=0=879....877 and 891 primes
n=1=809 primes
n=2=741... 739 and 741 primes
n=3=677 primes
n=4=615...613 and 617 primes
n=5=557 primes
n=6=501...499 and 503 primes
n=7=449 primes
n=8=399...397 and 401 primes
n=9=353 primes
n=10=309...307 and 311 primes
n=11=269 primes
n=12=231... 229 and 233 primes
n=13=197 primes
n=14=165...163 and 167 primes
n=15=137 first
n=16=111...109 and 113 primes
n=17=89 primes
n=18=69...67 and 71 primes
n=19=53 primes
n=20=39...37 and 41 primes
n=21=29 primes
n=22=21...19 and 23 primes
n=23=17 primes
n=24=15...13 and 17 primes

 

n=0=15...13 and 17 primes
n=1=17 prime
n=2=21...19 and 23 primes
n=3=29 prime
n=4=39...37 and 41 primes
n=5=53 prime
n=6=69...67 and 71 primes
n=7=89 prime
n=8=111...109 and 113 prime
n=9=137 prime
n=10=165...163 and 167 primes
n=11=197 prime
n=12=231... 229 and 233 primes
n=13=269 prime
n=14=309...307 and 311 primes
n=15=353 prime
n=16=399...397 and 401 primes
n=17=449 prime
n=18=501...499 and 503 primes
n=19=557 prime
n=20=615...613 and 617 primes
n=21=677 prime
n=22=741...739 and 743 primes
n=23=809 prime
n=24=879...877 and 881 primes
n=25=953 prime

 


Q. Can you find better functions alike than the two already given above?


From Dec 14-20 2024, contributions came from Michel Branicky

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Michael wrote:

ceil(1.5*n^2 -78*n + 1029) produces 26 integers with the property.

n=1: 953 prime
n=2: 879 ... 877 and 881 primes
n=3: 809 prime
n=4: 741 ... 739 and 743 primes
n=5: 677 prime
n=6: 615 ... 613 and 617 primes
n=7: 557 prime
n=8: 501 ... 499 and 503 primes
n=9: 449 prime
n=10: 399 ... 397 and 401 primes
n=11: 353 prime
n=12: 309 ... 307 and 311 primes
n=13: 269 prime
n=14: 231 ... 229 and 233 primes
n=15: 197 prime
n=16: 165 ... 163 and 167 primes
n=17: 137 prime
n=18: 111 ... 109 and 113 primes
n=19: 89 prime
n=20: 69 ... 67 and 71 primes
n=21: 53 prime
n=22: 39 ... 37 and 41 primes
n=23: 29 prime
n=24: 21 ... 19 and 23 primes
n=25: 17 prime
n=26: 15 ... 13 and 17 primes

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