A062500 Duplicate of A007965.
1, 1, 118, 13983, 48667074, 13055867207, 232630103648534, 144115171092292831
Offset: 1
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n=1: a(1) = prime(1)^prime(1+1) - prime(1+1)^prime(1) = 2^3 - 3^2 = 8 - 9 = -1. n=3: a(3) = prime(3)^prime(4) - prime(4)^prime(3) = 5^7 - 7^5 = 78125 - 16807 = 61318.
[NthPrime(n)^NthPrime(n+1)-NthPrime(n+1)^NthPrime(n): n in [1..10]]; // Vincenzo Librandi, Nov 02 2014
seq(ithprime(i)^ithprime(i+1)-ithprime(i+1)^ithprime(i), i=1..20); # Robert Israel, Nov 02 2014
Array[Prime[ # ]^Prime[ #+1]-Prime[ #+1]^Prime[ # ]&,16] (* Vladimir Joseph Stephan Orlovsky, Oct 11 2009 *)
a(1) = (1-1)^F(1) - F(1)^(1-1) = 0^1 - 1^0 = 0 - 1 = -1; a(4) = (4-1)^F(4) - F(4)^(4-1) = 3^3 - 3^3 = 27 - 27 = 0; a(5) = (5-1)^F(5) - F(5)^(5-1) = 4^5 - 5^4 = 1024 - 625 = 399.
Table[(n-1)^Fibonacci[n] - Fibonacci[n]^(n-1), {n, 1, 12}] (* Georg Fischer, Apr 11 2023 *)
For n = 1, a(n) = n^prime(n!) - prime(n!)^n = 1^2 - 2^1 = -1.
[n^NthPrime(Factorial(n)) - NthPrime(Factorial(n))^n: n in [0..6]]; // Vincenzo Librandi, Sep 15 2015
Table[n^Prime[n!] - Prime[n!]^n, {n, 0, 4}] (* Michael De Vlieger, Sep 14 2015 *)
a(n) = n^prime(n!) - prime(n!)^n; vector (6, n, a(n-1))
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