cp's OEIS Frontend

A131939 Least k such that the difference between consecutive 3-almost primes A014612(k) equals n, or 0 if no such k exists.

%I A131939 #12 Mar 03 2025 20:29:29
%S A131939 5,3,13,1,10,2,4,31,32,36,12,7,136,19,302,486,1094,73,1366,6763,1092,
%T A131939 2006,8924,4785,18345,18487,42798,16571,11095,57831,60912,4528,24846,
%U A131939 41304,232350,233678,123279,1779265,740729,177385,1015228,1772286
%N A131939 Least k such that the difference between consecutive 3-almost primes A014612(k) equals n, or 0 if no such k exists.
%C A131939 Index of smallest 3-almost prime gap equal to n. This is to 3-almost primes A014612 as A123375 is to semiprimes A001358. a(25) = 0 or a(25) > 10000. Conjecture: a(n) > 0 for all n.
%F A131939 a(n) = MIN{k such that A114403(k) = n, or 0 if no such k exists}.
%F A131939 a(n) = MIN{k such that A014612(k+1) - A014612(k) = n, or 0 if no such k exists}.
%e A131939 a(1) = 5 because A014612(6)-A014612(5) = 28-27 = 1.
%e A131939 a(2) = 3 because A014612(4)-A014612(3) = 20-18 = 2.
%e A131939 a(3) = 13 because 66-63 = 3.
%e A131939 a(4) = 1 because 12-8 = 4.
%e A131939 a(5) = 10 because 50-45 = 5.
%e A131939 a(6) = 2 because 18-12 = 6.
%e A131939 a(7) = 4 because 27-20 = 7.
%e A131939 a(8) = 31 because 138-130 = 8.
%e A131939 a(9) = 32 because 147-138 = 9
%e A131939 a(10) = 36 because 164-154 = 10.
%t A131939 p3=Select[Range[2*10^6],PrimeOmega[#]==3&];s={};Do[d=0;Until[p3[[d+1]]-p3[[d]]==n,d++];AppendTo[s,d],{n,37}];s (* _James C. McMahon_, Mar 02 2025 *)
%Y A131939 Cf. A014612, A114403, A123375.
%K A131939 nonn
%O A131939 1,1
%A A131939 _Jonathan Vos Post_, Oct 05 2007
%E A131939 More terms from _R. J. Mathar_, Oct 07 2007