cp's OEIS Frontend

A321169 a(n) is the smallest prime p such that p + 2 is a product of n primes (counted with multiplicity).

%I A321169 #27 Jan 11 2019 15:05:37
%S A321169 3,2,43,79,241,727,3643,15307,19681,164023,1673053,885733,2657203,
%T A321169 18600433,23914843,100442347,358722673,645700813,4519905703,
%U A321169 18983603959,48427561123,31381059607,261508830073,1307544150373,3295011258943,24006510600883,12709329141643,53379182394907,190639937124673,2615579937350539
%N A321169 a(n) is the smallest prime p such that p + 2 is a product of n primes (counted with multiplicity).
%C A321169 a(n) ~ c * 3^n. - _David A. Corneth_, Jan 11 2019
%H A321169 David A. Corneth, <a href="/A321169/b321169.txt">Table of n, a(n) for n = 1..801</a>
%e A321169 a(1) = 3 as 3 + 2 = 5 (prime),
%e A321169 a(2) = 2 as 2 + 2 = 4 = 2*2 (semiprime),
%e A321169 a(3) = 43 as 43 + 2 = 45 = 3*3*5  (3-almost prime),
%e A321169 a(4) = 79 as 79 + 2 = 81 = 3*3*3*3 (4-almost prime).
%t A321169 ptns[n_, 0] := If[n == 0, {{}}, {}]; ptns[n_, k_] := Module[{r}, If[n < k, Return[{}]]; ptns[n, k] = 1 + Union @@ Table[PadRight[#, k] & /@ ptns[n - k, r], {r, 0, k}]]; a[n_] := Module[{i, l, v}, v = Infinity; For[i = n, True, i++, l = (Times @@ Prime /@ # &) /@ ptns[i, n]; If[Min @@ l > v, Return[v]]; minp = Min @@ Select[l - 2, PrimeQ]; If[minp < v, v = minp]]] ; Array[a, 10] (* after _Amarnath Murthy_ at A073919 *)
%o A321169 (PARI) a(n) = forprime(p=2, , if (bigomega(p+2) == n, return (p))); \\ _Michel Marcus_, Jan 10 2019
%o A321169 (PARI) a(n) = {my(p3 = 3^n, u, c); if(n <= 2, return(4 - n)); if(isprime(p3 - 2), return(p3 - 2)); forprime(p = 5, oo, if(isprime(p3 / 3 * p - 2), u = p3 / 3 * p - 2; break ) ); for(i = 2, n, if(p3 * (5/3)^i > u, return(u)); for(j = 1, oo, if(p3 * j \ 3^i > u, next(2)); if(bigomega(j) == i, if(isprime(p3 / 3^(i) * j - 2), u = p3 / 3^(i) * j - 2; next(2) ) ) ) ); return(u) } \\ _David A. Corneth_, Jan 11 2019
%Y A321169 Cf. A001222, A001358, A014612, A014613, A014614, A046306, A046308, A046310, A046312, A046314, A073919, A118883.
%K A321169 nonn
%O A321169 1,1
%A A321169 _Amiram Eldar_ and _Zak Seidov_, Jan 10 2019