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 A239472 Least number k such that k^n-(k-1)^n-...-3^n-2^n is prime. a(n) = 0 if no such number exists. 6
 2, 3, 3, 7, 3, 0, 0, 0, 0, 7, 7, 0, 4, 0, 8, 11, 3, 16, 15, 0, 4, 7, 0, 23, 0, 19, 12, 11, 3, 0, 3, 7, 12, 0, 12, 0, 0, 0, 0, 0, 16, 0, 0, 0, 59, 11, 44, 32, 16, 0, 0, 0, 3, 0, 23, 0, 20, 75, 3, 0, 28, 0, 0, 0, 36, 0, 60, 0, 0, 0, 36, 0, 0, 0, 0, 19, 0, 0, 0, 0, 0, 91, 75, 0, 0, 0, 32, 108, 7, 0, 60, 0, 40, 39, 0, 0, 0, 0, 80 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) = 0 for n = {6, 7, 8, 9, 12, 14, 20, 23, 25, ...} because for k large enough, k^n-(k-1)^n-...-3^n-2^n < 0. Thus, no number will be prime. See A240083 for the n-values with nonzero entries. LINKS EXAMPLE 2^2 = 4 is not prime. 3^2-2^2 = 5 is prime. Thus, a(2) = 3. 2^3 = 8 is not prime. 3^3-2^3 = 19 is prime. Thus, a(3) = 3. PROG (Python) import sympy from sympy import isprime def Lep(n): ..for k in range(2*10**3): ....num = k**n ....for i in range(2, k): ......num -= i**n ......if num < 0: ........return None ....if isprime(num): ......return k n = 1 while n < 100: ..if Lep(n) == None: ....print(0) ..else: ....print(Lep(n)) ..n += 1 (PARI) a(n)=k=1; while((s=k^n-sum(i=2, k-1, i^n))>0, if(isprime(s), return(k)); k++) for(n=1, 100, print1(a(n), ", ")) \\ Derek Orr, Mar 12 2015 CROSSREFS Cf. A240083. Sequence in context: A111003 A289277 A140182 * A234943 A209494 A082910 Adjacent sequences:  A239469 A239470 A239471 * A239473 A239474 A239475 KEYWORD nonn AUTHOR Derek Orr, Mar 31 2014 STATUS approved

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Last modified October 23 06:48 EDT 2019. Contains 328335 sequences. (Running on oeis4.)