cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A288507 Least number k such that both prime(k+1) -/+ prime(k) are products of n prime factors (counting multiplicity).

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