A390829 - OEIS

%I #38 Nov 28 2025 16:10:46

%S 5989,15673,263029,445189,480253,648769,668353,992029,1096753,1246873,

%T 1288273,1648633,1849999,2224003,2248393,2362603,2484373,3158383,

%U 3590419,3787879,5334403,5496529,6519019,6718603,6919573,6968281,7148083,7397779,8138119,9157333,10307083

%N Initial values of 8 semiprimes in arithmetic progression with common difference 4.

%C For all n, a(n), a(n)+4, a(n)+8, a(n)+12, a(n)+16, a(n)+20, a(n)+24, a(n)+28 are semiprimes.

%C No such 9-tuple; i.e., semiprimes from x to x+32, exists.

%F a(n) == 1 (mod 6).

%p N:= 6*10^7: # for terms <= N

%p P:= select(isprime,[seq(i,i=3..(N+28)/3,2)]):

%p S:= {}:

%p for i from 1 do

%p   p:= P[i]; m:= (N+28)/p; if m < p then break fi;

%p   j:= ListTools:-BinaryPlace(P,m);

%p   S:= S union convert(map(`*`,P[i..min(j+1,nP)],p),set)

%p od:

%p S2:= S intersect map(`-`,S,4):

%p S4:= S2 intersect map(`-`,S2,8):

%p S8:= S4 intersect map(`-`,S4,16):

%p sort(convert(S8,list)); # _Robert Israel_, Nov 23 2025

%t okQ[k_]:=AllTrue[Range[k,k+28,4],PrimeOmega[#]==2&];Select[Range[10^6],okQ] (* _James C. McMahon_, Nov 28 2025 *)

%o (PARI) is_a390829(n) = forstep(k=n, n+28, 4, if(bigomega(k)!=2, return(0))); 1 \\ _Hugo Pfoertner_, Nov 23 2025

%Y Cf. A001358, A082919, A124570, A125025.

%K nonn

%O 1,1

%A _Soko Kosaka_, Nov 21 2025