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 A243269 Smallest prime p such that p^k - 2 is prime for all odd exponents k from 1 up to 2*n-1 (inclusive). 0
 5, 19, 31, 201829, 131681731, 954667531, 8998333416049 (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: A006512 : Primes p such that p - 2 is also prime. A240126 : Primes p such that p - 2 and p^3 - 2 are also prime. A242517 : Primes p such that p - 2, p^3 - 2 and p^5 - 2 are primes. A242518 : Primes p such that p - 2, p^3 - 2, p^5 - 2 and p^7 - 2 are primes. LINKS EXAMPLE For n = 1, p = 5, p - 2 = 3 is prime. For n = 2, p = 19, p - 2 = 17 and p^3 - 2 = 6857 are primes. For n = 3, p = 31, p - 2 = 29, p^3 - 2 = 29789, and p^5 - 2 = 28629149 are primes. 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. A006512, A240126, A242517 and A242518. Sequence in context: A347531 A356716 A262700 * A252930 A031019 A324557 Adjacent sequences: A243266 A243267 A243268 * A243270 A243271 A243272 KEYWORD nonn,hard,more AUTHOR Abhiram R Devesh, Jun 02 2014 EXTENSIONS a(7) from Bert Dobbelaere, Aug 30 2020 STATUS approved

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Last modified February 7 22:10 EST 2023. Contains 360132 sequences. (Running on oeis4.)