A242886 Smallest prime p_n which generates n primes of the form (p^i + 2) where i represents the first n odd numbers.
3, 3, 419, 132749, 514664471, 1164166301, 364231372931
Offset: 1
Examples
For n = 1, p = 3 generates primes of the form p^n + 2; for i = 1, p + 2 = 5 (prime). For n = 2, p = 3 generates primes of the form p^n + 2; for i = 1 and 3, p + 2 = 5 (prime) and p^3 + 2 = 29 (prime). For n = 3, p = 419 generates primes of the form p^n + 2; for i = 1, 3, and 5, p + 2 = 421 (prime), p^3 + 2 = 73560061 (prime), and p^5 + 2 = 12914277518101 (prime).
Programs
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Python
import sympy ## isp_list returns an array of true/false for prime number test for a ## list of numbers def isp_list(ls): pt=[] for a in ls: if sympy.ntheory.isprime(a)==True: pt.append(True) return(pt) co=1 while co < 7: al=0 n=2 while al!=co: d=[] for i in range(0,co): d.append(int(n**((2*i)+1))+2) al=isp_list(d).count(True) if al==co: ## Prints prime number and its corresponding sequence d print(n,d) n=sympy.ntheory.nextprime(n) co=co+1
Extensions
a(7) from Bert Dobbelaere, Aug 30 2020
Comments