A397411 - OEIS

%I #35 Jul 02 2026 18:28:00

%S 6,14,20,75,74,115,114,298,1240,1239,1238,10741,13273,62236,62235,

%T 102085,1290984,6692394,10323095,10323094,15808857,61111603,164877079,

%U 603332885,1356788897,1356788896,1356788895,1356788894,1356788893,6409098262

%N Smallest number k such that bigomega(k+i) and omega(k+i), for i=0..n, but not for i=n+1, are both prime.

%C a(28) = 1356788893, a(29) = 6409098262. a(n) is nonprime. Let p be the largest prime < a(n). Let q be the smallest prime >= a(n). Then q - p >= n + 2. - _David A. Corneth_, Jun 24 2026

%e a(0) = 6 as both bigomega(6+0) = 2 and omega(6+0) = 2 are prime but not both bigomega(6+0+1) and omega(6+0+1) are prime. 6 is the smallest number having this property. - _David A. Corneth_, Jun 24 2026

%e a(1) = 14 as bigomega(14) = 2 and omega(14) = 2 are both prime, bigomega(15) = 2 and omega(15) = 2 are both prime and bigomega(16) = 4 is not prime and omega(16) = 1 is not prime. 14 is the smallest number having this property.

%Y Cf. A001221, A001222, A396852.

%K nonn,more,new

%O 0,1

%A _Jean-Marc Rebert_, Jun 24 2026