A243885 Smallest prime p_n which generates n primes of the form (p_n^i - 4) when i runs through the first n odd numbers.
7, 11, 11, 971, 71394923, 959316767, 13342820302307
Offset: 1
Examples
a(1) = 7 because 7-4 = 3 (prime), a(2) = 11 because 11-4 = 7 (prime) and 11^3 - 4 = 1327 (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 > 0: al=0 n=2 while al!=co: d=[] for i in range(0, co): d.append(int(n**((2*i)+1))-4) 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(6) from Bert Dobbelaere, Jul 16 2019
a(7) from Giovanni Resta, Jul 18 2019
Comments