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Primes of form p^q+q^p+1, where p, q are also primes.
1

%I #5 May 26 2024 00:51:37

%S 2531,94933,48989177,19088056323407827075424486287615602692671561637,

%T 10027860709531471276608129899567499096303854889970269316268113271,

%U 88537996291958256446260440678593208943077817551131498658191653913030830300434060998128240895267

%N Primes of form p^q+q^p+1, where p, q are also primes.

%e a(1) = 3^7+7^3+1 = 2531;

%e a(2) = 5^7+7^5+1 = 94933;

%e a(3) = 5^11+11^5+1 = 48989177;

%e a(4) = 3^97+97^3+1 = 19088056323407827075424486287615602692671561637;

%e a(5) = 23^47+47^23+1.

%t a[n_] := Block[{}, For[l = {}; i = 1, i < n, i++, For[j = i, j < n, j++, p = Prime[i]; q = Prime[j]; x = p^q + q^p + 1; If[PrimeQ[x], l = Append[l, x]]]]; Print[Sort[Union[l]]]]; a[50]

%t Union[Select[First[#]^Last[#]+Last[#]^First[#]+1&/@Tuples[Prime[Range[50]],2],PrimeQ]] (* _Harvey P. Dale_, Oct 17 2014 &)

%Y Cf. A118097.

%K nonn

%O 1,1

%A Cheng Zhang (cz1(AT)rice.edu), Jan 26 2010