A240082 Numbers m such that k^m - (k-1)^m - ... - 3^m - 2^m - 1 is prime for some k.

2, 3, 4, 5, 6, 7, 8, 12, 13, 16, 17, 19, 31, 34, 48, 61, 68, 72, 89, 107, 112, 124, 127, 236, 260, 288, 384, 396, 432, 520, 521, 576, 607, 1080, 1244, 1279, 1424, 1500, 1660, 2203, 2281, 2640, 2730, 2808, 3190, 3217, 4150, 4253, 4423, 4428, 5016, 5892

Offset

1,1

Comments

These are the values of m such that A240081(m) is nonzero.

Links

Table of n, a(n) for n=1..52.

Prog

(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 < 10**3:
  if Leq(n) != None:
    print(n)
  n += 1
(PARI) f(n)=for(k=1, 10^3, num=k^n; for(i=2, k-1, num-=i^n; if(num<1, return(0))); if(ispseudoprime(num-1), return(k))); n=1; while(n<10^3, if(f(n), print(n)); n+=1)

Crossrefs

Cf. A240081.

Sequence in context: A383248 A032972 A210585 * A321334 A342044 A238084

Adjacent sequences: A240079 A240080 A240081 * A240083 A240084 A240085

Keyword

nonn

Author

Derek Orr, Mar 31 2014

Extensions

a(34)-a(52) from Giovanni Resta, Apr 02 2014

Status

approved