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Numbers k such that k+i^2, i=0..6 are all semiprimes.
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%I #30 Feb 02 2025 04:28:39

%S 3238,4162,4537,13918,16837,17857,18673,24553,55477,62353,78457,84358,

%T 92878,102838,106813,129838,135853,140002,142822,146722,148318,151957,

%U 166177,180013,184213,187933,194338,210637,214393,231757,242698,271198,274393,305677

%N Numbers k such that k+i^2, i=0..6 are all semiprimes.

%e 3238 is a term because 3238=2*1619; 3239=41*79; 3242=2*1621; 3247=17*191; 3254=2*1627; 3263=13*251; 3274=2*1637.

%p q:= n-> andmap(x-> numtheory[bigomega](x)=2, [n+i^2$i=0..6]):

%p select(q, [$1..400000])[]; # _Alois P. Heinz_, Mar 06 2023

%t okQ[k_] := AllTrue[Table[k+i^2, {i, 0, 6}], PrimeOmega[#] == 2&];

%t Select[Range[400000], okQ] (* _Jean-François Alcover_, Feb 02 2025 *)

%o (PARI) isok(k) = sum(i=0, 6, bigomega(k+i^2)==2) == 7;

%Y Subsequence of A070552.

%Y Cf. A001358 (semiprimes).

%K nonn

%O 1,1

%A _Alexandru Petrescu_, Mar 06 2023