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 A242886 Smallest prime p_n which generates n primes of the form (p^i + 2) where i represents the first n odd numbers. 0
 3, 3, 419, 132749, 514664471, 1164166301 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The first 4 entries of this sequence are the first entry of the following sequences: a. A001359: Lesser of twin primes. b. A240110: Primes p such that p + 2 and p^3 + 2 are also prime. c. A242326: Primes p for which p + 2, p^3 + 2, and p^5 + 2 are also prime. d. A242327: Primes p for which (p^n) + 2 is prime for n = 1, 3, 5, and 7. LINKS EXAMPLE 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). PROG (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 CROSSREFS Cf. A001359, A240110, A242326, A242327. Sequence in context: A009715 A335258 A292163 * A221947 A138662 A009011 Adjacent sequences:  A242883 A242884 A242885 * A242887 A242888 A242889 KEYWORD nonn,hard,more AUTHOR Abhiram R Devesh, May 25 2014 STATUS approved

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Last modified August 4 06:58 EDT 2020. Contains 336201 sequences. (Running on oeis4.)