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%I #8 Mar 14 2015 18:28:36
%S 1033,1049,1193,1553,2393,3833,6353,10433,11633,12473,19793,25673,
%T 38273,50753,52553,55313,59053,67073,95273,98993,101513,114593,158633,
%U 197273,215393,300233,376793,381713,427433,459353,553073,620393,735473,787793
%N Primes of the form p^2 + q^10 where p and q are primes.
%C p and q cannot both be odd. Thus p=2 or q=2. There are rarer primes of the form 2^2 + q^10 such as 2^2 + 3^10 = 59053 and 2^2 + 5^10 = 9765629 and 2^2 + 13^10 = 137858491853. Hence most solutions are of the form 2^10 + q^2 and (except for rarer solutions such as 5^2 + 2^10 = 1049 and 2^2 + 5^10 = 9765629, no more with the larger prime under 100) are congruent to 3 mod 10.
%F {a(n)} = {p^2 + q^10 in A000040 where p and q are in A000040}.
%e a(1) = 3^2 + 2^10 = 1033.
%e a(2) = 5^2 + 2^10 = 1049.
%e a(3) = 13^2 + 2^10 = 1193.
%e a(4) = 23^2 + 2^10 = 1553.
%t Take[Select[Sort[Table[Prime@p^2 + Prime@q^10, {p, 200}, {q, 3}] // Flatten], PrimeQ@# &], 34] (* _Robert G. Wilson v_, Sep 26 2006 *)
%Y Cf. A000040, A045700 Primes of form p^2+q^3 where p and q are prime, A122617 Primes of form p^3+q^4 where p and q are primes.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Sep 23 2006
%E More terms from _Robert G. Wilson v_, Sep 26 2006
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