A390829 Initial values of 8 semiprimes in arithmetic progression with common difference 4.

5989, 15673, 263029, 445189, 480253, 648769, 668353, 992029, 1096753, 1246873, 1288273, 1648633, 1849999, 2224003, 2248393, 2362603, 2484373, 3158383, 3590419, 3787879, 5334403, 5496529, 6519019, 6718603, 6919573, 6968281, 7148083, 7397779, 8138119, 9157333, 10307083

Offset

1,1

Comments

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.

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

Links

Table of n, a(n) for n=1..31.

Formula

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

Maple

N:= 6*10^7: # for terms <= N
P:= select(isprime, [seq(i, i=3..(N+28)/3, 2)]):
S:= {}:
for i from 1 do
  p:= P[i]; m:= (N+28)/p; if m < p then break fi;
  j:= ListTools:-BinaryPlace(P, m);
  S:= S union convert(map(`*`, P[i..min(j+1, nP)], p), set)
od:
S2:= S intersect map(`-`, S, 4):
S4:= S2 intersect map(`-`, S2, 8):
S8:= S4 intersect map(`-`, S4, 16):
sort(convert(S8, list)); # Robert Israel, Nov 23 2025

Mathematica

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

Prog

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

Crossrefs

Cf. A001358, A082919, A124570, A125025.

Sequence in context: A233871 A182295 A028546 * A055108 A046903 A171351

Adjacent sequences: A390826 A390827 A390828 * A390830 A390831 A390832

Keyword

nonn

Author

Soko Kosaka, Nov 21 2025

Status

approved