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%I A365537 #22 Dec 26 2023 03:51:54
%S A365537 4,34,51,55,1169,6641,18751,204929,101249,2490751,6581249,68068351,
%T A365537 262986751,1842131969,9601957889,13858918399,145046192129,75389157377,
%U A365537 18444674957311,39806020354049,124758724247551,878616032837633,551785225781249
%N A365537 a(n) is the first semiprime k such that k-1 and k+1 each have exactly n prime factors (counted with multiplicity).
%C A365537 a(n) is the least k such that A001222(k)  = 2 and A001222(k - 1) = A001222(k + 1) = n.
%e A365537 a(3) = 51 because 51 = 3 * 17 is a semiprime and 50 - 1 = 50 = 2 * 5^2 and 51 + 1 = 52 = 2^2 * 13 are triprimes.
%p A365537 V:= Vector(10): count:= 0:
%p A365537 b:= 1: c:= 2:
%p A365537 for x from 5 while count < 10 do
%p A365537   a:= b; b:= c; c:= numtheory:-bigomega(x);
%p A365537   if b = 2 and a = c and V[a] = 0 then
%p A365537     count:= count+1; V[a]:= x-1; printf("%d %d\n",a,x-1);
%p A365537   fi
%p A365537 od:
%p A365537 convert(V,list);
%t A365537 seq[len_, kmax_] := Module[{s = Table[0, {len}], k = 2, c = 0, m}, While[c < len && k < kmax, If[PrimeOmega[k] == 2, m = PrimeOmega[k - 1]; If[m <= len && s[[m]] == 0 && PrimeOmega[k + 1] == m, c++; s[[m]] = k]]; k++]; s]; seq[10, 10^7] (* _Amiram Eldar_, Sep 08 2023 *)
%Y A365537 Cf. A001222, A001358.
%K A365537 nonn
%O A365537 1,1
%A A365537 _Zak Seidov_ and _Robert Israel_, Sep 08 2023
%E A365537 a(14) from _Amiram Eldar_, Sep 08 2023
%E A365537 a(15)-a(23) from _Martin Ehrenstein_, Dec 26 2023

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