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A240081
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Least number k such that k^n-(k-1)^n-...-3^n-2^n-1 is prime.
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2
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0, 2, 2, 5, 2, 6, 2, 5, 0, 0, 0, 6, 2, 0, 0, 6, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0
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OFFSET
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1,2
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COMMENTS
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a(n) = 0 for n = {1, 9, 10, 11, 14, 15, 18...} because at certain k-values, k^n-(k-1)^n-...-3^n-2^n-1 becomes a strictly decreasing negative sequence. Thus, no number will be prime.
See A240082 for the n-values with nonzero entries.
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LINKS
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EXAMPLE
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2^4-1 = 15 is not prime. 3^4-2^4-1 = 64 is not prime. 4^4-3^4-2^4-1 = 158 is not prime. 5^4-4^4-3^4-2^4-1 = 271 is prime. Thus, a(4) = 5.
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MATHEMATICA
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a[n_] := Block[{s=1, k=1}, While[s > 0 && ! PrimeQ[s], s -= 2*k^n; s += (++k)^n]; If[s > 0, k, 0]]; Array[a, 90] (* Giovanni Resta, Apr 01 2014 *)
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PROG
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(Python)
import sympy
from sympy import isprime
def Leq(n):
..for k in range(1000):
....num = k**n
....for i in range(2, k):
......num -= i**n
......if num < 1:
........return None
....if isprime(num-1):
......return k
n = 1
while n < 100:
..if Leq(n) == None:
....print(0)
..else:
....print(Leq(n))
..n += 1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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