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%I #22 Jul 24 2017 01:55:14
%S 24,319,738,57360,1077529,116552943
%N Least number k such that both prime(k+1) -/+ prime(k) are products of n prime factors (counting multiplicity).
%C Prime(k) + prime(k+1) cannot be semiprime, so the offset is 3.
%C For n=3 to 8, all terms k happen to satisfy prime(k+1) - prime(k) = 2^n. - _Michel Marcus_, Jul 24 2017
%e n = 8: k = 116552943, p = prime(k) = 2394261637, q = prime(k+1) = 2394261893; both q-p = 2^8 and p+q = 2*3^2*5*7^3*155119 are 8-almost primes (A046310).
%o (PARI) a(n) = my(k = 1, p = 2, q = nextprime(p+1)); while((bigomega(p+q)!= n) || (bigomega(p-q)!= n), k++; p = q; q = nextprime(p+1)); k; \\ _Michel Marcus_, Jul 24 2017
%o (Python)
%o from sympy import factorint, nextprime
%o def A288507(n):
%o k, p, q = 1, 2, 3
%o while True:
%o if sum(factorint(q-p).values()) == n and sum(factorint(q+p).values()) == n:
%o return k
%o k += 1
%o p, q = q, nextprime(q) # _Chai Wah Wu_, Jul 23 2017
%Y Cf. A001043, A001223, A046310, A251600.
%K nonn,more
%O 3,1
%A _Zak Seidov_, Jun 10 2017
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