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A335667 a(n) is the smallest even number k such that k-1 and k+1 are both n-almost primes. 1

%I

%S 4,34,274,2276,8126,184876,446876,18671876,95234374,1144976876,

%T 6018359374,281025390626,2068291015624,6254345703124

%N a(n) is the smallest even number k such that k-1 and k+1 are both n-almost primes.

%C 10^13 < a(15) <= 181171630859374. - _Giovanni Resta_, Jun 21 2020

%H David A. Corneth, <a href="/A335667/a335667.gp.txt">Upper bounds on a(n) for n = 1..37 where values with * are proven values</a>

%e a(1) = 4 since 4 - 1 and 4 + 1 are both primes.

%e a(2) = 34 since 34 - 1 = 33 = 3*11 and 34 + 1 = 35 = 5*7 are both semiprimes.

%e a(3) = 274 since 274 - 1 = 273 = 3*7*13 and 274 + 1 = 275 = 5^2 * 11 are both 3-almost primes.

%t m = 8; v = Table[0, {m}]; c = 0; o1 = 1; n = 4; While[c < m, o2 = PrimeOmega[n + 1]; If[o1 == o2 && v[[o1]] == 0, c++; v[[o1]] = n]; o1 = o2; n += 2]; v

%Y Cf. A001222, A088077, A115186, A154704.

%K nonn,more

%O 1,1

%A _Zak Seidov_ and _Amiram Eldar_, Jun 17 2020

%E a(12)-a(14) from _Giovanni Resta_, Jun 21 2020

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Last modified May 8 12:48 EDT 2021. Contains 343666 sequences. (Running on oeis4.)