Σάββατο, 27 Δεκεμβρίου 2014

ANOPOLIS PRIMES

Pn = n + Qk, n is a natural number (including 0) ie n belongs to No = {0, 1, 2, 3, ....} with n > 0

where Qk is the smallest number in the set No - {Q1, Q2,.... Qk-1} such that Pn is prime

n = 1

Q1 = the smallest number in the set No - {Q0} = No - {0} such that 1 + Q1 is prime = 1

P1 = 1 + 1 = 2

n = 2

Q2 = the smallest number in the set No - {Q0, Q1} = No - {0, 1}such that 2 + Q2 is prime = 3

P2 = 2 + 3 = 5

n = 3

Q3 = the smallest number in the set No - {Q0, Q1, Q2} = No - {0, 1, 3} such that 3 + Q3 is prime = 2

P3 = 3 + 2 = 5

n = 4

Q4 = the smallest number in the set No - {Q0, Q1, Q2, Q3} = No - {0, 1, 3, 2} such that 4 + Q4 is prime = 7

P4 = 4 + 7 = 11

and so on.

Pn : 2, 5, 5, 11, 11, 11, 11, 17, 17, 23, 23, 23, 23, 29, 29, 37, 37, 37, 37, 37, 37, 47, 47, 47, 47, 53, 53, 59, 59, 59, 59, 59, 67, 67, 67, 67, 73, 73, 79, 79, 83, 83, 83, 83, 89, 89, 97, 97, 97, 97, 97, 97,.....

Anopolis Prime Numbers Sequence:

An = the missing primes from Pn: 3, 7, 13, 19, 31, 41, 43, 61, 71,.............................

Antreas P Hatzipolakis, 27 Dec. 2014

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