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%I #10 Jan 06 2023 10:43:43
%S -1,-1,152,2224,9056,108736,-1,4532992,34674176,268684288,2280249344,
%T 18693763072,138890141696,1111848828928,8803419521024,70375767212032,
%U 564861779443712,4507018424221696,36030079546425344,288238419152207872,2305850719072157696,18446757709572210688,147573952867129622528
%N a(n) is the least number that is the sum of two cubes of primes and is 2^n times an odd prime, or -1 if there is no such number.
%C a(n) is the least term of A086119 such that a(n)/2^n is an odd prime, or -1 if there is no such term.
%C Since p^3 + q^3 = (p+q)*(p^2 - p*q + q^2), we must have p+q = 2^n, and p^2 - p*q + q^2 an odd prime.
%C Is a(n) > 0 for all n > 7?
%e a(3) = 152 because 3^3 + 5^3 = 152 = 2^3 * 19, 3 and 5 are primes and 19 is odd, and no smaller number works.
%p f:= proc(n) local p,q,t;
%p t:= 2^n; p:= nextprime(t/2);
%p while p > 2 do
%p p:= prevprime(p);
%p q:= t - p;
%p if isprime(q) and isprime(p^2 - p*q + q^2) then return p^3 + q^3 fi
%p od;
%p -1
%p end proc:
%p map(f, [$1..20]);
%Y Cf. A086119, A359448.
%K sign
%O 1,3
%A _Robert Israel_, Jan 01 2023
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