A154535 -id:A154535 - cp's OEIS frontend

A194566 Centered cube numbers: (n+1)^100+n^100.

1, 1267650600228229401496703205377, 515377520732011332304111729993850674198810727377, 1606938044259505653062694103672199063651968615055494942823377

Offset: 0

Jonathan Vos Post, Aug 29 2011

Can never be prime, and after a(0) must have at least 3 prime factors, as a(n) = (2*n^4 + 4*n^3 + 6*n^2 + 4*n + 1) * p_16(n) * p_80(n).

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Cf. A036085-A036102, A100267, A154535, A100266, A152913, A194155, A194185, A194216, A194553.

a:= n-> (n+1)^100 +n^100: seq (a(n), n=0..20);

Total/@Partition[Range[0,5]^100,2,1] (* Harvey P. Dale, Aug 10 2013 *)

a(n) = (n+1)^100 + n^100.

A244947 Least number k > n such that k^16 + n^16 is prime.

Original entry on oeis.org

2, 85, 4, 33, 6, 7, 8, 13, 22, 13, 16, 41, 28, 15, 22, 19, 24, 23, 54, 31, 22, 27, 56, 61, 38, 29, 40, 37, 34, 61, 32, 35, 82, 35, 46, 43, 40, 49, 58, 67, 42, 55, 58, 49, 46, 61, 58, 61, 68, 73, 92, 63, 94, 77, 166, 57, 82, 63, 72, 109, 76, 121, 82, 79, 86, 67, 72, 77, 82, 71, 98

Offset: 1

Derek Orr, Jul 08 2014

nonn

a(n) = n+1 iff n is in A154535.

			10^16 + 11^16 = 55949729863572161 is not prime. 10^16 + 12^16 = 2^16*(5^16+6^16) is not prime. 10^16 + 13^16 = 675416609183179841 is prime. Thus a(10) = 13.

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Cf. A158979, A089489, A242554.

a(n)=for(k=n+1,10^4,if(isprime(k^16+n^16),return(k)))
n=1;while(n<100,print1(a(n),", ");n++)

import sympy
from sympy import isprime
def a(n):
  for k in range(n+1,10**4):
    if isprime(k**16+n**16):
      return k
n = 1
while n < 100:
  print(a(n),end=', ')
  n += 1

cp's OEIS Frontend

A194566 Centered cube numbers: (n+1)^100+n^100.

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